Shark NV581 vs NV583
images from manufacturer

The only difference between Shark NV581, NV581Q, and NV583 is the accessories they come with, otherwise they are the same.

Shark Navigator Powered-Lift-Away NV581 includes a Pet Multi-Tool, Duster Crevice Tool, and Dust-Away Hard Floor Attachment with 1 Microfiber Pad.
Shark Navigator Powered Lift-Away DLX NV581Q includes a Pet Multi-Tool, Duster Crevice Tool, Dust-Away Hard Floor Attachment with 1 Microfiber Pad, and Canister Caddy.
Shark Navigator Powered Lift-Away Deluxe NV583 includes a Pet Multi-Tool, Duster Crevice Tool, Dust-Away Hard Floor Attachment with 1 Microfiber Pad, Appliance Wand, plus Pet Power Brush.

The Pet Multi Tool is a 2 in 1 cleaning tool. The hard bristle brush remove debris off surfaces, and the upholstery tool is for removing pet hair from upholstery.
The Duster Crevice Tool is also a 2 in 1 tool. You can use it as a crevice tool to clean tight areas or use it as a dusting brush.
The Dust-Away hard-floor attachment with a microfiber pad is designed for picking up and wiping away fine debris from hard floors.
The Canister Caddy allows you to transform your vacuum into a canister, so you do not have to carry the lift away pod while cleaning.
The Appliance Wand helps to clean areas under hard-to-move appliances and furniture.
The Pet Power Brush helps remove pet hair and dirt from upholstery and carpeted surfaces.

Shark NV501 vs NV752
images from manufacturer

Both of the Shark Rotator Professional Lift Away NV501 and Shark Rotator Powered Lift Away True Pet NV752 are 3 in 1 vacuum cleaner – upright, canister, lift away.
They are bagless, feature HEPA filter, swivel head, LED headlights, and detachable handle. However, there are also some differences between NV501 and NV752.

The NV752 has more convenient control.
The NV752 has fingertip control Power Button which is located on the handle whereas NV501 has the power switch on the top of the pod.
And the NV752 has the cleaning mode control on the handle so you do not have to bend down to touch any button to switch between cleaning modes whereas the NV501 does not have the control on the handle.

Brushroll On/Off Switch
The NV501 has a BRUSHROLL button next to the Power button which is on the top of the lift away pod, this Brushroll button allows you to turn on/off the brushroll. Whereas the NV752 does not have this Brushroll button, it has 1 hard floor cleaning mode with the brushroll off and 2 carpet/area rug cleaning mode with brushroll on.

Suction Control
The NV752 has no suction control slider or similar things. It has 3 cleaning modes that provides different suction power, the Hard Floor mode with brush off provides the strongest suction and the Thick Carpet/Area Rug mode with brush on produces the weakest suction.
The NV501 has a suction control collar on the handle that allows you to release suction when you need weak suction to clean delicate things.

Led light on handle
The NV752 has LED lights on the handle whereas the NV501 does not have.

Dust Bin Capacity
The nv752 dust cup holds 3.3 dry quarts whereas the NV501 can holds up to 3.1 dry quarts.

Included Tools
The NV752 comes with a TruePet Mini Motorized Brush, Hard Floor Genie, Caddy, Upholstery Tool, Dusting Genie, Dusting Brush, Accessories Bag.
The NV501 comes with a Pet Power Brush, Crevice Tool, Dusting Brush, Canister Caddy, Straight Suction Nozzle and a Wide Pet Upholstery Tool.

Warranty
The NV752 is backed by a 7 year limited warranty rather than 5 year warranty on the NV501.

Color
The NV501 comes in white with red whereas the NV752 is in Bordeaux.

Dimensions
The dimensions of NV501 are 45.7″ x 13.4″ x 12.2″ (H x W x D) versus 46″ x 12″ x 13″ on the NV752.

According to user reviews, the NV752 has bigger LED headlight, more flexible hose, more smoother wheels, better suction on the sides, and better build quality.

Learn more by reading manuals:
NV501 Manual – http://www.sharkclean.com/include/pdf/manual-NV500.pdf
NV752 Manual – http://www.sharkclean.com/include/pdf/manual-NV752.pdf

P.S. Shark NV500 series vacuum cleaners are similar items, NV750 series models are also similar.
The comparison info above is also helpful if you are looking for difference between Shark Rotator Professional Lift Away and Shark Rotator Powered Lift Away.

Shark NV682 vs NV752
These 2 Shark Rotator Powered Lift Away models are similar, both of them are 3-in-1 vacuum cleaner – Upright, Powered Lift-Away, Canister, however, they still have some differences that you may want to know before buying.

The main notable difference is the Size.
Shark NV752 is the original Shark Rotator Powered Lift-Away model, it is a full size upright, larger than the NV682 Shark Rotator Powered Lift Away Speed which is a compact size versatile vacuum.
The NV752 has larger dust cup capacity – 3.3 quarts versus 2.9 quarts (not sure if it’s accurate) on the NV682.
The NV752 is slightly larger. According to Shark, the dimensions of NV752 are 46″ x 12″ x 13″(H x W x D) versus 46″ x 12″ x 12″ on the NV682.
The NV752 is heavier, full upright vacuum weighs 15.6 pounds, lift away pod weighs about 8 pounds whereas the NV682 full upright weighs 13.3 pounds and lift away mode weighs less than 6 pounds.

There are also some design differences.
If you look closer, you can find that the handles are different.
The NV752 has LED light on the handle whereas the NV682 has NO lights on the handle.
The NV752 has a Power Switch on the top of the handle whereas the NV682 has no Power Button on the handle, instead, its power button is on the vacuum pod.
On the NV752 handle, there are 3 cleaning modes to select – Hard Floor, Carpet/Low Pile, and Thick Carpet/Area Rug modes. Whereas the Speed model NV682 has 2 modes – Hard Floor and Carpet.
And here comes another difference – Suction Control.
The NV752 has NO variable suction control on the handle which the NV682 has.
It seems that switch for the 3 cleaning modes is the only suction control on the NV752, the Hard Floor mode provides the highest suction with brushroll off, the Carpet/Low Pile mode provides high suction with motorized brushroll on, and the Thick Carpet/Area Rug mode provides low suction with motorized brushroll on.
While using the NV682, you can choose between Hard Floor and Carpet modes, then adjust the suction power with the suction control slider on the front of the handle to meet your cleaning needs.

Other differences.

Power Specifications
The technical specifications of the NV752 are 120V, 60Hz, 1150W, 9.5A versus 120V, 60Hz, 800W, 6.7A on the NV682.

Color
NV752 is Bordeaux whereas the NV682 is Blue.

Accessories Included
The NV752 comes with a TruePet Mini Motorized Brush, Hard Floor Genie, Caddy, Upholstery Tool, Dusting Genie, Dusting Brush, Accessories Bag.
The NV682 comes with a TruePet Mini Motorized Brush, Dust-Away Pro cleaner head, Caddy, Duster Crevice, Pet Multi-Tool.

P.S.
The Shark NV750, NV750w, NV751, and NV753 are identical to NV752 except for the color and accessories.
The Shark NV680, NV681, NV683 are the same as NV682 except for the color and the tools they come with.
So, if you are looking for info about the differences between these Shark Rotator Powered Lift-Away / True Pet Model / Deluxe Model and Speed Models, the above info is also helpful to you.

Shark NV682 Manual – http://www.sharkclean.com/include/pdf/manual-NV682.pdf
Shark NV752 Manual – http://www.sharkclean.com/include/pdf/manual-NV752.pdf

image from manufacturer

The Shark Rotator Powered Lift-Away Speed NV680 series are versatile vacuum cleaners. The two notable differences between NV680, NV681, NV682 and NV683 are the color and the tools they come with. Except for that, they are the same.

The Shark NV680 is green, comes with Dust-Away Pro cleaner head, Duster Crevice and Pet Multi-Tool.

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The Shark NV681 is green, comes with Dust-Away Pro cleaner head, Pet Power Brush, Duster Crevice and Pet Multi-Tool.
The Shark NV682 is blue, comes with Dust-Away Pro cleaner head, TruePet Mini Motorized Brush, Duster Crevice, Pet Multi-Tool and Canister Caddy.
The Shark NV683 is blue, comes with Dust-Away Pro cleaner head, Home and Car Detail Tool, Canister Caddy, Duster Crevice and Pet Multi-Tool.

Dust-Away Pro cleaner head is designed for hard-floor cleaning.
Duster Crevice is a 2 in 1 tool for cleaning crevice and dusting.
Pet Power Brush is for removing pet hair and dirt from carpeted stairs and upholstery.
TruePet Mini Motorized Brush is for picking up pet hair, debris, and dander out of upholstery and surfaces.
With the Canister Caddy, the NV682 and NV683 vacuum cleaners can transform from an upright or powered lift away into a canister vacuum.
Home and Car Detail Tool for tiny cleaning jobs in tight area.

Same things they have – LED headlights to illuminate dark spots, fingertip floor controls on the handle, swivel steering, Anti-Allergen Complete Seal Technology + HEPA filter, motorized brush, 30 feet power cord, full vacuum weighs 13.3 lbs, 12 inches cleaning width, 6.7 amps.

Due to the different accessories they include, there is also price difference between these Rotator Powered Lift-Away Speed models.

If you know more differences between them, please share below.

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You can also read more by downloading manuals from Shark official site:
NV680 manual – http://www.sharkclean.com/include/pdf/manual-NV680.pdf
NV681 manual – http://www.sharkclean.com/include/pdf/manual-NV681.pdf
NV682 manual – http://www.sharkclean.com/include/pdf/manual-NV682.pdf
NV683 manual – http://www.sharkclean.com/include/pdf/manual-NV683.pdf