To expand on Metal God's question for my own clarification:
Since SCOTUS granted certerathingIcan'tspell, and then tossed it back to lower courts, isn't that in effect saying: "You got it wrong, get it right or we will overrule you"?
Certiorari is the word you're looking for. That said, you've described SCOTUS' actions in language very similar to what I've used. Basically, it said, "These are wrong. Here's your new rule. Try again."
Now, with respect to vacating the appellate court rulings, .... What that means, to use language I've seen in some rulings, is that the appellate court rulings are 'held for naught.' In other words, it's like they never happened. An example not pulled from any of the cases at bar: Let's say a case went to the U.S. District Court for the Northern District of California (a federal court), and that court struck a law as unconstitutional, and then went to the 9th Circuit Court of Appeals. Let's further say that the 9th Circuit reversed, holding it constitutional, and was appealed to SCOTUS. If SCOTS then grants cert, and vacates the judgment of the 9th, then the case goes back to the 9th, but the holding of the U.S. District Court for the Northern District of CA goes back into effect, to include any stays in effect when it went up on appeal the first time.
Now, let's not all jump for joy just yet. There are several possible procedural paths a case could take. Some examples that build on the one in the preceding paragraph: (1) The 9th Circuit could reach the same decision as before (constitutionality), but try to do so in a way that complies with Bruen. (2) The 9th Circuit could decide that it lacked an adequate historical record and send it back for development of the historical record. or (3) The 9th could affirm the holding of the U.S. District Court.
The question then becomes whether we want to win or lose at the 9th. This may seem like a silly question, but consider this: (a) if we win at he 9th, the state could decide not to appeal, and the decision is only binding in the 9th Circuit, but possibly persuasive in other circuits; (b) if we lose at the 9th, our side gets the option of appeal and if we then go on to win at SCOTUS, we get a decision that is binding law on all of the circuits.
Let me also add that we may be in for what I think of as the "fermentation period," like we had after Heller and MacDonald. It is entirely possible that SCOTUS will let cases "ferment" in the circuits, watching to see what they come up with and waiting until we've got enough conflict between appellate court decisions to require a SCOTUS ruling to harmonize them.