The column still has a base. The base is just sitting on the thingamajig. Sorry too lazy at the moment to look up or think of what the thingamajig is actually called lol.
Can the thing underneath / supporting the base be called a corbel?
Also, I was reading that a column in the wall would be called an 'applied column', and it would only be a pilaster if it was rectangular? Maybe the term pilaster is used more widely now.