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: 
Something none of the answers have pointed out yet is that the meaning of *apartment* is **different** in New York City and in most of the rest of the U.S. In New York City, an *apartment* is a single unit in a multi-unit residential building, regardless of whether you rent or own it, and of whether the ownership is legally a condo or co-op arrangement (so *apartment* in NYC means the same thing that *flat* means in the U.K.). In most of the rest of the U.S., an *apartment* is a *rented* single unit in a multi-unit residential building. 

This means that in most of the U.S., if you live in a multi-unit residential building, you either live in an apartment, a co-op, or a condo. In New York City, and in much of Canada, your *apartment* will either be a rental, a co-op, or a condo (or a sublet, if you lease it from somebody who in turn is renting it themself).
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.