What size CPVC for bathtub fixture

I have a question related to my other post, Plumbing question - converting copper to CPVC. The instructions for installing the fixture say to use 1/2" IPS pipe or 1/2" copper. Is IPS the same thing as CPVC? Is the 1/2" the Inside Diameter? I have some 1/2" PVC (not CPVC) that I used on drain pipes and it measures about 11/16" Inside Diameter and 13/16" Outside Diameter. It says 1/2" on the side of it, but nothing is 1/2" so I'm totally confused about why it says 1/2". I bought some 1/2" CPVC (which says 1/2" on the side of it) and it measures about 7/16" Inside Diameter and 5/8" Outside Diameter. Is this the right stuff to use on the bathtube fixture?

Here is a picture of what I have now. The copper is about 5/8" Outside Diameter.

Here is a (blurry) picture of the copper to CPVC adapter. The package says: Tube to Male Pipe Connector, 5/8" x 1/2"

Here's a picture of the new bathtub fixture and a 1/2" pipe to 1/2" CPVC adapter screwed into one of the fittings.

Danny,
Looks like you are good to go with your set-up.
The copper is ½" and that looks like the right fitting to convert to CPVC

Thanks Jerry. I guess I'll never understand how they came up with the way they catagorize this stuff. Nothing measures 1/2", either Inside Diameter or Outside Diameter.