Just touching the ball...no.

so this only applies when a person is not "saving" a ball from going oob?

Applies to any player who intentionally goes out of bounds, returns, and is the first to touch the ball.

So in summary ---

NFHS casebook 7.1.1 -- says legal you can be first to touch
&
NCAA 9-4-1 --says illegal you can't be first to touch?

You do not understand the difference between going out of bounds because you momentum takes you out of bounds and running out of bounds to get some kind of advantage or on purpose?

Saving the ball is not going out on your own volition or to get a clear advantage. Running around a screen is or running around someone to beat someone to the ball is also apart of that rule.

Peace

No.

well, it's correct that those plays / rules say what you indicate. But, they are referring to two different plays, so you can't make a comparison.

A better comparison would be FED 9.3.3B and NCAA AR 219

No, you're mixing two different things. NFHS 7.1.1 Situation D (a) would be the same in both codes.

Fed says if you go OOB intentionally, the ball is dead immediately.

NCAA-M says if you go OOB intentionally, return, and are the first to touch the ball then it's a violation.

Here's the NCAA case:
A.R. 219:

Team A sets a double screen for A1, who leaves the playing court voluntarily and runs under the basket, circles around, returns to the playing court and then is the first to receive the ball.

RULING: A violation has been committed by A1 for leaving the playing court and then becoming the first player to touch the ball upon return.

NFHS 7.1.1 applies exactly the same in NCAA.

NCAA 9-4-1 applies to "PURPOSEDLY" going OOB and returning. In NCAA it's only a violation if you are the next person to catch the pass. In NFHS is an immediate violation.

You are mixing up 2 entirely different rules/concepts.