Both of these 2 upright vacuum cleaners have the cord rewind system, but do not have a brush On/Off switch. To clean bare floor, you have to adjust the height setting to hard floor cleaning.
There is slight difference between them.
From the comparison, we can find that Hoover UH70820 features WindTunnel 2 technology while the UH70120 featues WindTunnel technology, this might be the major difference.
Hoover UH70820 has a bulkier handle part than the UH70120.
And they come in different colors.

Compare Hoover UH70820 and UH70120

	Hoover UH70120 WindTunnel T-Series Rewind Plus Bagless Upright Vacuum Cleaner	Hoover UH70820 WindTunnel® 2 Rewind Bagless Upright
Design	Upright	Upright
Price	$129.99 at Hoover.com on August 9, 2014	$129.99 at Hoover.com on August 9, 2014
Bagged or Bagless	Bagless	Bagless
Cord Length	27 ft	25 ft
Auto Cord Rewind	Yes	Yes
Amps	12 Amps	12 Amps
Motorized Brushroll	Yes	Yes
Brushroll On/Off	No	No
Motor Volts		1500 Volts
Height Adjustment Type	Manual, 5 Settings	5 position manual settings
Washable Filter	Yes	Yes
HEPA Filtration	Yes	Yes
Headlight	No	No
Weight	16.5 lbs	not specified
Cyclonic Action	Dual	Dual
WindTunnel Technology	WindTunnel	WindTunnel 2
Performance Check Indicator	Yes	Yes
Nozzle Width	13.5"	13.5"
Edge Cleaning	No	No
Self-propelled	No	No
Handle	D-Shaped Handle	D-Shaped Handle
Deep Recline Handle	No	No
Hose Type	stretch hose	stretch hose
Hose Length	8'	not specified
Included Tools	Air Powered Hand Tool, Crevice Tool, Dusting Brush	Air Powered Hand Tool, Crevice Tool, Dusting Brush
Cleaning Wand	Yes	Yes
Color	Gray and Green	Black and Red
Warranty	2 year limited warranty	2 year limited warranty
Manual	download manual	download UH70820 manual

If you know other difference between UH70120 and UH70820, please share below.