I am glad to hear there is no difference between 9mm and 9mm +p brass. Different case volumes would mess up everything!
Oh, you've misunderstood. The good news is that a +P marking doesn't mean less case volume. The bad news is that case volumes are not the same across headstamps. So instead of having some nice, cross-brand indication that case volume is reduced or that web strength is increased (such as a +P marking).... you just have whatever a particular manufacturer thinks is appropriate!
In other words, there are different case volumes. It's just much harder to figure it out than some standardization of +P brass might involve!