HOB = Hang on back filter, as it would hang on the back of your tank.
ex.
HOB FILTER
Canister filter = a filter that sits below the tank that has a containment chamber for water to flow thru, and then pushed back into the tank.
ex.
CANISTER FILTER
I had some problems understanding the acronyms myself when I first started posting here
For a 20G I suggest
Penguin Bio-wheel 200
MARINELAND.COM - CONSUMER PRODUCTS
It says it is for a 50G but it really is right for a 20G. Is your 20G a long, standard, or high? (the dimensions)
If you have a stand I really recommend a canister filter. I recently upgraded to the magnum 350 and it made a HUGE difference.