The difference between Apt and Condo is the ownership.

Apt. is owned by a person or company who rent the property out to other people.The people who lives in an Apt. doesn't have ownership. The people who lives in a condo is the property's owner.(sometimes the condo owner also rent the property to other people.)

The difference bewtween Apt. Condo with Townhouse is the style of building. The concept of townhouse usaully compare with single house.