Question: I have never really understood the connotation of someone calling their domicile a *condo* over the word *apartment*. I have a vague feeling the former is fancier and more up-scale, but are there any real differences I'm not aware of?

Answer: 
I'd say that an apartment is any single dwelling in a multi-unit building. I wouldn't consider the two halves of a duplex to be apartments, nor would a townhouse unit be considered an apartment. But if a house was divided up into units, they would each be considered apartments.

Condo, which is short for condominium, is mostly the subset of apartments where the individual living units are owned by different people. That isn't to say that the actual people living in each unit own the unit, because they may be renting from someone else that owns the individual unit. Also, townhouses can be condominiums.

Condominiums also have the concept of having shared facilities and maintenance costs, in which the individual unit owners also have an interest. Generally, the condominium complex has a corporation which owns it, and the individual owners are participants in it to some degree.
Condos tend to be in complexes rather than single buildings. Additionally, a condo is purchased and owned, whereas an apartment is rented.

[This Link](http://www.realtor.com/Basics/AllAbout/HomeAffordability/Condo.asp) has some good info about condos.