CPVC pipe is probably more generally used now for residential and light industrial plumbing than the plain PVC. Addition of the chlorination is a "post production" process that allows tailoring of properties for a more consistent product and/or for improvement of specific properties for a particular use. Special properties can be achieved, although the ordinary stuff at the lumber yard has consistent, if more ordinary, properties suitable for most plumbing uses.

For an outdoor plumbing use, as implied for a pool, CPVC usually will have a higher softening point than PVC's ~105F useful limit. Without flow to cool it internally, plumbing laying in the sun can reach much higher temperatures and both pipe life and safety could be compromised. (I've measured "surface temps" of 195F on "things laying in the sun" fairly frequently, and some much higher on special occasions.)

CPVC is commonly available, and some consider it easier to work with than PVC. A "better adhesive" is recommended, but it's not significantly more expensive than for PVC.

In my area, CPVC is preferred for most new residential plumbing, and for major/significant remodelling, even if the pipes won't see outside environmental effects. Either is still a choice you can make if the whim grabs you.

John