I don't live in Columbia, but the Columbia sub-forum may be a better place to ask.
Bear in mind to better assist you they will need to know what your monthly budget is and the basic area your jobs may be in.
A condo and apartment are pretty much the same thing. The difference is condos are typically owned by an individual that rents them and an apartment is owned by a company that rents them. Most apartments are single story 1-3 bedroom units in a building that is 1-3 stories high. Think really big hotel.
Townhomes are typically multi-floor units who, like condos, if rented is often done so by the owner. Think of stand alone homes pushed together so they share exterior side walls.
You may see a reference to a 'patio home'. This is typically like townhomes, but on a single story.
The Columbia Area sub-forum can be found here:
http://www.city-data.com/forum/columbia-area/