As far as I know, they are almost the same except for the color , the accessory, and the price.
DC39 animal is in PURPLE while DC39 is in YELLOW.
And the DC39 animal comes with a mini turbine head for picking up pet hair from tight areas while DC39 doesn’t have this tool. And DC39 Animal is more expensive than DC39 Multi Floor canister vacuum.
Otherwise, they are the same.
Contact Dyson customer service to confirm this if you want.

You can compare Dyson DC39 and DC39 animal with the following comparison chart and find the difference between them.

Dyson DC39 Multi Floor vs Animal
Vacuum Pics:	image from manufacturer	image from manufacturer
Vacuum:	DC39 Multi Floor Vacuum Cleaner	Dyson DC39 Animal Vacuum Cleaner
Color:	Yellow	Purple
Type:	Canister	Canister
Movement type:	Ball Technology	Ball Technology
Warranty:	5 Year Warranty- parts and labor	5 Year Warranty- parts and labor
Price:
Rating:
Specifications and Features:
Brushbar control type:	Controlled at the handle.	Controlled at the handle. No bending down required.
Weight:	22.9 pounds	22.9 pounds
Product Dimensions(H x D x W):	14.2 x 10.2 x 19.5 inches	14.2 x 10.2 x 19.5 inches
Tools / Accessories:	Stair tool; Combination accessory tool; Triggerhead floor tool	Stair tool; Combination accessory tool; Mini turbine head; Triggerhead floor tool
Suction Power:
Power Cord Length:	21.3 ft	21.3 ft
Power Rating:	275 Air Watts	275 Air Watts
Filtration:
Filter:	HEPA filter	HEPA filter
Dirt Collection:
Bag Type:	Bagless	Bagless
Bin Capacity:	0.53 gallons	0.53 gallons
Other:
	Radial Root Cyclone technology – Patented Dyson technology that improves suction power and traps more dirt. Ball technology and central steering system mechanism for easy control. Comes with a mini turbine head for cleaning tight areas like stairs and autos. Adjustable wand for high reach cleaning.