The hard fork between Bitcoin and Bitcoin cash was done in part to increase the processing limit from 1 megabyte to 8 megabytes
Between BTC and BCH? No, the hard fork only happen on Bitcoin Cash.
A minor semantic note:
It is entirely accurate to say that there was a fork between Bitcoin and Bitcoin Cash. A hard fork is a split in the chain at a particular point as the result of an incompatible change. It is not the change itself. In this case, one side of the fork is Bitcoin and the other side is Bitcoin Cash. Sure, the incompatible change was made by Bitcoin Cash, but it was still a fork between Bitcoin and Bitcoin Cash, regardless.