The NCAA rule book definition of a jump stop (see Rule 4-44 below) does not include catching the ball and landing on 2 feet. Similarly, while the NFHS rule book does not include the term jump stop, rule 44-2-b.2 specifically states ...
if one foot foot is on the floor ...

The player may jump off that foot and simultaneously land on both.

This is the implicit NFHS definition of a jump stop and is totally consistent with the explicit NCAA definition.

NCAA Definition:

Section 44. Jump Stop
Art. 1. A jump stop is executed when a player catches the ball while moving
or dribbling with:
a. One foot on the playing court, jumps off that foot and lands
simultaneously on both feet (no pivot foot).
80 RULE 4 / DEFINITIONS
b. Two feet off the playing court, lands on one foot, jumps off that foot
and lands simultaneously on both feet (no pivot foot).
Art. 2. A jump stop may also be executed when the dribbler has one foot on
the playing court, initiates a jump off that foot, ends the dribble with both
feet off the playing court and lands simultaneously on both feet (either foot
can be established as the pivot foot).

All true...but many (maybe most) coaches use the term for the move described by bob. Since it is commonly used for both types of moves, it is often necessary to distinguish between the two whenever the term is discussed.

Really? What about:
That's exactly to what I was refering. Sorry if it wasn't clear (basketball is over, for now, for me, so all my posts are without specific references at hand).

Note that this example is preceded by a jump from the pivot foot. It is the jump from the pivot foot THEN landing on both feet simultaneously that makes for a jump stop.

Just because others are calling something else a jump stop doesn't make it so. We could go on forever about incorrect basketball terms.

(BTW, thanks to IndianaRef for the clarification.)

I suggest that you re-read all of Article 2 carefully. You left off the beginning which states the dribbler has one foot on the playing court, initiates a jump off that foot.

The bottom line is that by explicit NCAA rule definition and implicit NFHS definition, a jump stop involves jumping off of one foot (and therefore previously landing on one foot) and then landing on 2 feet. Simply catching the ball in the air and landing simultaneously on 2 feet does not constitute a jump stop.

Art. 2. A jump stop may also be executed when the dribbler has one foot on the playing court, initiates a jump off that foot, ends the dribble with both feet off the playing court and lands simultaneously on both feet (either foot can be established as the pivot foot).

Yes, when I said "catch", I meant "end the dribble in the air". It was the example / play / movie in my head, so it was clear to me.

In any event, it's a difference without a distinction. Either foot can be the pivot foot in either case.

In the "other" type of jump stop (catching the ball or ending the dribble on one foot, or landing on one foot and then jumping and landing on both), neither foot can be the pivot foot.

The point is that when someone asks a question about a jump stop, the correct answer often depends on their definition of jump stop.

So . . .

Player A is dribbling towards the basket and leaves the floor with both feet while dribbling and then gathers the ball once in the air (pro hop, jump stop, whatever you want to call it) landing with both feet simultaneously.

They may then pivot, moving one foot towards the basket and follow that by letting both front and back foot leave the floor to shoot without traveling.

Correct.

That can be a problem. When people can simply make up definitions to suit themselves, it can only cause confusion and rule myths for everyone else.

Panther's example is certainly a legal move, but it's not a jump stop. While the NFHS doesn't have a definition, the NCAA does, and I believe that's one we should all adopt. While I've never heard of any confusion over "jump stop," it may not be a bad idea to get that term into Rule 4.

In the end, it's all about being on the same page.

Do you have something that gives Panther's move a name?

We just have to accept that, sometimes, there will be terminology in use that doesn't precisely match the book. This term is so widely used to describe both moves that there is no point in arguing that one is not a jump stop....they both are.

It is simply the legal establishment and subsequent legal movement of a pivot foot. It is not a jump stop. The original poster posed the question of is it legal to take a step after a jump stop. The answer is unequivocally no for 4 of the major rules codes (NFHS, NCAA, NBA and FIBA). The WNBA rules explicitly allow it.

As bainsey alluded to, this discussion points to the importance of using definitions as provided by the rules bodies rather than as commonly assumed by coaches and others.

Try this name - Hop Stop
 

When training on the legal pivot movements around a jump stop, I refer to the play where the player catches the ball in the air (catches on a pass, rebound, or ends dribble) lands on one foot and then alights to 2 feet simultaneously as a "HOP STOP". This is a subset of all Jump stops - difference being when control of the ball is established before landing on (alighting off) 1 foot or after landing on one foot.

Now you got the idea. Forget about "jump stops" or "hop steps"(whateverthehell they are), etc. completely and just call "traveling".

T-R-A-V-E-L-I-N-G!!

That way we won't have stoopid 2-page discusions like these that just confuse newer officials.

I don't know about newer officials but I know there were plenty of officials scratching their heads at the NCAA preseason meetings.
To me the key take away point is when the pivot foot is established. If you get that, it makes the play somewhat easier. It is a tough move to describe, it is a sort of "have to see it" play.
As a federal judge and a congressman were famously quoted "I can't tell you what it is, but I know it when I see it" (paraphrased, sorry Mr Flint):)

Jacobellis v. Ohio 378 U.S. 184 (1964)
 

"I shall not today attempt further to define the kinds of material I understand to be embraced within that shorthand description (hard-core pornography); and perhaps I could never succeed in intelligibly doing so. But I know it when I see it, and the motion picture (The Lovers) involved in this case is not that." (Justice Potter Stewart, regarding obscenity)

I'm definitely not going to post an image here.