A condo is a form of ownership, is short for the word condominium, it can be a free standing home, an attached home or a multi story building with individual units, sometimes an apartment complex (a rental unit) that has been converted to individual unit ownership.
A Townhouse is a mulit story property attached or free standing that consist typically of a 1st and 2nd floor at a minimum.
Aparatment is not a form of ownership but a rental orf a studio (no bedrooms) 1,2,3,4, etc bedroom property.
Multi family home, in the north east usally consist of a duplex (side by side) decker (one on top of another) from 2 units to 4 seperate rental units, above that it becomes an apartment.
Single family home is just that, One structure that is individually owned.