When are “carpet” and “rug” synonymous?

I am a speaker of Canadian English. Recently, I saw this video on Youtube about operant conditioning link to video where the speaker says

"remove something pleasant like the carpet.”

at about 1.03 into the video just as the animation shows someone pulling a rectangle of cloth out from under the dog. But, isn’t that called a rug?

So my question is, why does she say "carpet" in that video? Or is she simply incorrect? I know when I say carpet, I mean the whole floor covering that can’t be moved. But then again, I think about Aladdin and the magic carpet (but really it is a rug!) So, when can we use carpet and rug interchangeably?

I believe that carpet is a hypernym of rug. That is to say that rugs may be carpets but that not all carpets are rugs. In terms of sets, which I find useful for analysis of meaning, the set of carpets contains the set of rugs. From this perspective, some rugs may be carpets, and the two are then synonymous, although there is no general synonymy.

Cambridge

carpet:

thick, woven material for covering floors, or a piece of this material

Some support for the above suggestions may be found in these slightly different definitions of rug:

Cambridge

Rug:

a piece of thick heavy cloth smaller than a carpet, used for covering the floor or for decoration

Merriam Webster

Rug:

a piece of thick heavy fabric that usually has a nap or pile and is used as a floor covering

Lexico

Rug:

A floor covering of thick woven material or animal skin, typically not extending over the entire floor.