That is a very generic question, but let me try to answer it.
Clay removes the above surface contaminants. These are things that can somewhat be felt on the surface of the paint.
A paint cleaner or cleaner wax removes the buildup of dirt or film that settles on the paint. This cannot really be felt but can be seen especially on lighter cars. The cleaner is chemical based. Surely clay does remove some of this, but not all.
Then there are also pure paint cleaners that are specifically designed to remove any wax or sealant, or polish residue to leave the paint "pure" for coatings or sealants.
Claying alone doesnt totally clean the paint. Cleaners alone also do not totally clean the paint. A combination of both virtually will.
I hope that makes sense.