At this moment, the only place you can find the NV370 model is on Amazon. Even at Shark official website, you cannot find any info about it.
Amazon call the NV370 The Shark Navigator Lift-Away Pro Special Edition. A special edition of the Navigator Lift-Away Pro. What makes it special is the Gentle Deep Clean Technology with Superior Carpet Cleaning, and it is approved by the CRI (The Carpet and Rug Institute http://www.carpet-rug.org/About-CRI.aspx).

According to the info listed on Amazon, the only difference between NV370 and NV356E is the Brush Roll they come with. The NV370 features Premium Brush Roll whereas the NV356E uses Standard Brush Roll.
Then what’s the difference between the Standard Brush Roll and the Premium Brush Roll? The Shark customer service did not answer clearly on this. They just said that they are associated with different models. And they told me that the only difference between the NV356E and the NV370 is where they sold. They did not mention anything about the Gentle Deep Clean Technology or the Brush Roll.
Shark definately have to improve customer satisfaction. I find that many people always get confused by the similar product versions. At least, they should make the products info more clearly to save customers time on choosing a right model.

If you know other difference between these 2 Shark Navigator Lift-Away Pro versions, please share it below.

These are 2 different types of vacuum cleaners.
Shark Rocket (HV300, HV301, HV302, etc.) is a 2-in-1 vacuum, you can use it as an upright vacuum to clean from bare floors to carpets; or you can detach the floor nozzle and use it as a handheld to do some small quick pick ups around your house and cars.
Whereas the Shark Rocket Professional (NV480, NV482, NV484, etc.) is a slim and lightweight upright vacuum that could replace your bulky/heavy vacuum cleaner.

Shark Rocket vs Shark Rocket Professional

	Shark Rocket	Shark Rocket Pro
Design	Upright, Handheld 2 in 1	Upright
Bagged or Bagless	Bagless	Bagless
Dust Cup Capacity	0.472 dry quarts	0.8 dry quarts to the fill line and 1.8 dry quarts of real usable capacity
Corded or Cordless	Corded	Corded
Cord Length	Depending on the version you purchased, HV300 = 27', HV301 = 30', HV302 = 30', HV302Q = 30', HV300W = 32'	30'
Power	120V., 60Hz, 500 Watts, 4.2 Amps	120V., 60Hz, 700 Watts, 6 Amps
Brushroll Speeds	2 speeds, slow speed for cleaning bare floors and delicate area rugs, high speed for cleaning carpets.	brushroll has only one speed to clean carpets, and equip with a brushroll indicator to tell you if there is jam.
Weight	under 8 pounds	13 pounds
Dimensions	46" x 9.8" x 10.5" (H x W x D)	45.28" x 11.3" x 14.1"
Filtration	Washable Filters	Sealed vacuum technology with Washable HEPA Filter
HEPA Filter	No	Yes
Wall Mount	Yes	NA
Headlights	No	Yes
Swivel Steering	Yes	Yes
Suction Control	No	No
Color	Orange and Blue	steel gray with orange accents
Manual	Shark Rocket Manual Download Link from Official Site	Shark Rocket Pro Manual Download Link from Official Site

If you know other difference between Shark Rocket (HV300, HV301, HV302, HV302Q, HV300W) and Rocket Professional (NV480, NV482, NV484,…), please share below.

The difference between Shark Rocket NV480, NV482 and NV484 is the accessories they include, the vacuum body is identical.

Shark Rocket NV480 comes with a small 5.5″ Crevice Tool, Standard Crevice Tool, Dusting Brush, Small Turbo Brush.
NV482 includes a small 5.5″ Crevice Tool, long 18″ Flexi Crevice Tool, Dusting Brush, Small Turbo Brush and an Under Appliance Wand.
NV484 comes with a small 5.5″ Crevice Tool, long 18″ Flexi Crevice Tool, Dusting Brush, Small Turbo Brush, a Multi-Angle Dusting Brush and an Accessory Bag.
If you own these Shark Rocket Pro vacuum cleaners or know other difference between them, please share more details.
Here is a image that includes the tools, you can have a look at it below.

If you are interested in purchasing one or more of Shark Rocket Pro accessories, you can find them on Shark official website: http://www.sharkclean.com