At least in Postgres, table-valued functions can't take tables as arguments, only scalars. That's the main difference: functors can not just return tables, but take tables satisfying some interface as arguments.

https://www.postgresql.org/docs/7.3/xfunc-tablefunctions.htm...

I thought I had written a footnote or appendix about this but I guess I forgot.

MSSQL can take tables as arguments if they are temporary tables declared to be of a certain type. But that restriction limits their use a lot.