As, an "apartment" is a description of a physical thing, like a house or a factory or an igloo. A "condominium", however, is a legally defined term for a type of ownership structure.
In the old days, ownership of a residential dwelling was simple: there was a house, it held one family, and was owned by one person. Even when houses got bigger and the owner decided to rent out a room, there was no problem, it was still owned by one person, who gave a license to the tenant to occupy a portion of the structure.
This continued as apartment buildings first made their appearance: one person owned the structure, and rented out apartments to tenants.
But then one day someone wanted to own their apartment, rather than rent it. The problem is that real estate falls under a unique branch of the law, fundamentally based on the premise that every single piece of property is unique...because every single piece of the underlying land is unique. That's why you can buy or sell a house. But once you put two or more dwellings on the same piece of land, you've got a problem: although two people can jointly own the whole property, there's no way for them to own a specific apartment!
What to do?
The first solution was to work within the law as it existed, and that's where co-ops entered the picture. The term "co-op" is short for "co-operative corporation". Under this type of legal structure, if, say, ten people each want to own one apartment in a ten-unit building, they get together and form a corporation, which buys the building. But then the corporation gives a proprietary lease to each resident, allowing them the exclusive right to occupy a particular apartment. And because apartments can differ in value, the number of ownership shares of the co-op corporation can differ, based on the individual unit to which the proprietary lease related. The co-op structure (which first appeared in New York City around the beginning of the 20th century) had both advantages and disadvantages.
On the good side, the co-op corporation could itself go to a bank and get a traditional mortgage on the building, thereby significantly reducing the amount that each individual co-operator would have to pay for their apartment (although they would pay a higher monthly "maintenance fee" to the co-op corporation to cover their share of the mortgage payments.)
On the bad side, however, was the corollary: if one person failed to pay their maintenance fee when due, the corporation would be unable to make the full mortgage payment to the bank...and the bank could take possession of the building and throw everyone out! (This would clearly not be a Good Thing, and that's why co-ops have a reputation for being insanely tough and picky about who they let buy in to their building...sometimes even mandating 100% cash purchases.)
It seemed like there was no way around this conundrum given the way real estate law worked...so something was going to have to change. The result was the new, legally defined concept of the "condominium". Because the concept does not exist in traditional law, a jurisdiction (state or country, whoever is responsible for real estate law) must specifically pass a law defining what a condominium is, and authorizing it to be treated exactly as if it were real property.
Once that has been done, it is then possible to buy, sell, mortgage or rent individual apartments just like they were free-standing houses. But that still leaves the problem of what to do with the building's common areas, such as the corridors, elevators, basement, etc. Those, the condominium law continued, will all be owned by a single condominium corporation...which will charge each condo owner a fee each month for maintaining and operating the common areas.
Well, from here, things can get a tad complicated, as for example I live in a "cond-op", which is actually both! My building has a garage and retail stores in it, so the overall structure is owned as a condominium, but with only two owners: one company owns the garage and commercial spaces, and another owns the residential units. That second owner is...a co-op corporation, made up of the individual unit owners!!!!