@Jeruba There is a lot of terminology, and possibly people use the terms differently. It might even differ from state to state?
I think of Independent Living as a building or community that has apartments or houses that can be owned or rented depending on the particular Independent Living facility. They usually have services like shuttle buses to shopping and medical appointments, one or two meals a day, and the ability to step up to nursing care if they have that service, if that becomes necessary. If you own an apartment the ownership is not usually like regular full ownership, your heirs might not inherit the full value of your dwelling if you own it. People I know comment the sooner you move in the more value you get for your dollar if you want to own rather than rent. I have no idea if this is universal with Independent Living facilities, but something to be aware of as you look around.
Active Adult is governed by federal and state laws and in most states it is designated as a 55 and older community (a minimum of 80% of the community must be 55 or older) and no one under 19 can live there. This is what I think of as a retirement community. Some of them are simply condominiums or houses with age restrictions and not much more. No amenities, no activities, but the city you live in might have plenty to do. Some are massive communities like where I live with lots of amenities and classes. We have libraries, art studios, art classes, kilns for pottery and glass, and many other crafts, and that is all free/included. Then there are all the sizes in between. The ownership is just like owning any residential home, the key difference is no children can live in the Active Adult community.
In summary, I think the biggest difference is Independent Living has a “program” of sorts for its residents, while a basic retirement community is just saying no children can be full time residents and the communities come in many shapes and size. I’m not sure if I was helpful.