Condo is one sort of ownership structure in a multi-unit building. I imagine there are more than two, but co-op is the other structure that I'm familiar with.
"Condominium" also implies luxury (and especially new) apartments rather than mid-level or down market or generally older units.
The US basically has two kinds of multifamily development: dirt-cheap apartment blocks used to house the urban poor (as rentals), and luxury apartments built to cater to yuppies and investors (as a mix of rental and ownership). Essentially all “normal”/middle-class people live in detached houses in sprawl, where multifamily buildings are illegal. While homeownership is quite normal, the only urban homeowners are the rich. So almost all condos are high end.
There are many smaller suburban condominiums as well. These are typically much cheaper than luxury condos, and tend to be occupied by single parent families, the recently divorced, or retirees.
Some suburbs do not allow much apartment construction, but will allow these. They provide a more affordable lodging option that still contributes toward building equity.
"Condominium" also implies luxury (and especially new) apartments rather than mid-level or down market or generally older units.