[Torcert]

Why not something like: “God given natural and Civil rights?”

Those rights would fall under both classifications would they not?

[philman_36]

Why not something like: “God given natural and Civil rights?”
You're moving in the right direction, but natural rights are inherent (endowed/provided by our Creator) in all human beings simply because they're human beings and alive. However, an atheist wouldn't say their natural rights were endowed upon them by a Creator, would they? Yet they still have inherent natural rights so it's better to just say "natural rights".
And the Constitution recognizes our natural rights, it doesn't grant them.

Civil rights, on the other hand, are granted, both by Constitutional Amendment and by legislation. Constitutional Amendments and Major Civil Rights Acts of Congress

Those rights would fall under both classifications would they not?

Which rights, specifically, are you talking about when you say "those" and what do you mean by "classifications"? Your question is very vague.