Will a cut or a slot in a PCB change clearance or creepage?
You are correct:

Here is a nice picture of the definitions of creepage and clearance:



Note that adding a barrier will increase the clearance. Adding a barrier increases the physical length of insulated material between conductors, and that is what is considered when defining clearance. Normally a barrier is inserted into a slot (or slots) in the PCB.

Creepage and clearance are of great importance for high voltage isolation.