What is the difference between a condo and a townhouse?

Condo and Townhouse are architectural terms. Condos are like apartment buildings--they can have attached neighbors above, below, and at either side. Townhomes are like row houses. They ONLY have attached neighbors on the sides.
Condos and PUD (planned unit development) are both ownership terms. With condos, you own %100 from the unpainted walls of your unit in. You own in common the walls of the building, the land, and any other improvements like pools, laundry rooms, parking areas, etc. If there are 100 units in the building then you own 1/100 of the entire common area of the complex. 
A PUD is a development in which you own your home and the land it is on. You own in common with the other owners any common space, such as the roads, common landscaping, pools, and so forth that may be part of the development. A PUD can be a single family home OR a townhome.