Pass - Fumble
 

9-5-3 states that a player shall not dribble a second time after his/her first dribble has ended, unless it is after he/she lost control because of a pass or fumble which has then touched, or been touched by, another player.

Does this mean that a player, who has dribbled, may attempt a pass to another player and then, if the ball strikes the floor, legally retrieve it before it has been touched by another player? Or is the ball striking the floor the start of the second dribble? In this case, it is not a fumble but an attempted pass.

It depends on how you judge "attempt a pass." If it was a pass, then it's illegal to recover it. If it was a fumble, then it's legal to recover it.

I give the benefit of the doubt to "it was a pass."

This is the way that I have always interpreted it. But, why do you think NFHS chose to put "pass" along with "fumble" in 9-5-3?

I also get confused as to why the NFHS chooses to use "stop" in 4-44-2, 3 & 4.

I also am confused as to why the NFHS changed 4.15.4E to 4.44.3D in 08-09, making it a travel instead of an illegal dribble. It still looks like an illegal dribble to me.

Because if they didn't then even a pass that touched a defender could not be recovered and dribbled again.

I think you are confusing "recovering the ball" and "can not dribble again." In the case of the pass that isn't touched by a player (but hits the floor), they happen at the same time. In the case of a fumble, they are different things.

Re: 4-44

Maybe I don't understand your question? The traveling rule is defined in terms of the player's pivot foot. Having a pivot foot implies that the player is stopped. Not still, or motionless, but he is unable to move beyond the reach of his pivot foot. Consider the usage of "stop" as in "stop ball!", a common coaching command meaning to force the dribbler pick up his dribble during a fast break. When properly executed, the dribbler can no longer make direct progress toward the basket. He has been stopped.

4-44-2, in particular, contrasts stopping, and the optional and additional "step" of establishing a pivot foot, with moving or dribbling. So I take "stopped" to mean that the player is in one of the following positions: stationary with both feet on the floor, stationary with one foot on the floor and one in the air, pivoting with one foot on the floor, or both feet in the air and must pass/shoot/request timeout before returning to the ground. Moving would then be any other movement not allowed by 4-44. Such movements would include running, jumping, skipping, hopping (okay, I'm getting silly), cutting, back peddling, etc. without the ball, or similar movement with the ball while dribbling. In such movements, the player is unrestrained (as far as allowed by other rules, at least).

If I take the highlighted text in your quote as true, and I have no reason not to, then it makes sense to me. The red text belongs to BITS, the blue text belongs to scratch.