advanced french, what to play first: Qb6 or Nc6

The queen is not needed on c7.
The queen is needed on b6 to attack central pawn d4, the base of the white pawn chain d4-e5.

“It [the queen] is needed [on c7] if White never played d4 or took on c5”
Considering this is the ADVANCED FRENCH you’re asking about, White DID play d4. If 4. dxc5?? then simply 4… Bxc5 and 5… Qb6. If not, then 4… Qb6 and either 5… Bd7 or 5… Nc6.

You indeed don't need Qc7 in the Adanced French. She is typically best on b6, cause the d4 is the main target at first. I still play Nge7 instead, in order to get Nf5 immediately after. It is an interesting line, but Qb6 should be a bit more precise.

one reason to play qb6 first is to play certain sidelines, like the early bd7-bb5 line. You may play nc6 if you dont mind the main line, or for some reason like the old lines with early b6. They are also some restrictions on white when you choose one or the other

it is needed if white never played d4 OR took on c5
If White never played d4, you are not in an advance French and the question is irrelevant.
For the record, I have mentioned many times the plus of playing ...Qb6 first, but that is SPECIFICALLY in the Advance Variation after 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Qb6 5.Nf3 Nc6. This avoids the 5.Be3 line.
If d4 is not played, then the whole question is irrelevant, like in the KIA, you do not play Qb6 and Nc6. TOTALLY DIFFERENT LINE. 1.e4 e6 2.d3 d5 3.Nd2 Nf6 4.Ngf3 c5 5.g3 Nc6 6.Bg2 Be7 7.O-O O-O 8.Re1 b5 9.e5 Nd7 10.Nf1 a5 11.h4 b4 12.N1h2 Ba6 and now 13.Ng5 Qe8 or 13.Bf4 a4 or 13.Ng4 Nd4 (13...a4 is also possible here).
If White didn't play d4, you are not in an advance French. That's like someone telling you pancakes taste better with maple syrup. That doesn't mean you start putting maple syrup on everything you eat. Dare you to put maple syrup on your Filet Mignon and your mashed potatoes!
So if you are trying to take advice of one line and apply it to other lines, stop immediately. The French cannot be played in a cookie-cutter approach!

it is needed if white never played d4 OR took on c5
If White never played d4, you are not in an advance French and the question is irrelevant.
For the record, I have mentioned many times the plus of playing ...Qb6 first, but that is SPECIFICALLY in the Advance Variation after 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Qb6 5.Nf3 Nc6. This avoids the 5.Be3 line.
If d4 is not played, then the whole question is irrelevant, like in the KIA, you do not play Qb6 and Nc6. TOTALLY DIFFERENT LINE. 1.e4 e6 2.d3 d5 3.Nd2 Nf6 4.Ngf3 c5 5.g3 Nc6 6.Bg2 Be7 7.O-O O-O 8.Re1 b5 9.e5 Nd7 10.Nf1 a5 11.h4 b4 12.N1h2 Ba6 and now 13.Ng5 Qe8 or 13.Bf4 a4 or 13.Ng4 Nd4 (13...a4 is also possible here).
So if you are trying to take advice of one line and apply it to other lines, stop immediately. The French cannot be played in a cookie-cutter approach!
What is it called then? And what is the plan difference(except we are targeting e5 instead of d4)?

I always treated the pawn push like the inferior advanced variation. In my head the best thing white can do is to transpose back into the d4 line

it is needed if white never played d4 OR took on c5
If White never played d4, you are not in an advance French and the question is irrelevant.
For the record, I have mentioned many times the plus of playing ...Qb6 first, but that is SPECIFICALLY in the Advance Variation after 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Qb6 5.Nf3 Nc6. This avoids the 5.Be3 line.
If d4 is not played, then the whole question is irrelevant, like in the KIA, you do not play Qb6 and Nc6. TOTALLY DIFFERENT LINE. 1.e4 e6 2.d3 d5 3.Nd2 Nf6 4.Ngf3 c5 5.g3 Nc6 6.Bg2 Be7 7.O-O O-O 8.Re1 b5 9.e5 Nd7 10.Nf1 a5 11.h4 b4 12.N1h2 Ba6 and now 13.Ng5 Qe8 or 13.Bf4 a4 or 13.Ng4 Nd4 (13...a4 is also possible here).
So if you are trying to take advice of one line and apply it to other lines, stop immediately. The French cannot be played in a cookie-cutter approach!
What is it called then? And what is the plan difference(except we are targeting e5 instead of d4)?
The KIA vs French? You aren't targeting e5. You need that to remain closed to prevent the flood gates from opening by White. Your attack is on the queenside in the KIA vs French.
Did you all this time think the Tarrasch, Exchange, Advance, Classical, McCutchen, Winawer, Rubinstein, and King's Indian Attack all behaved the same simply because the first two moves for Black are the same? The Winawer is to the Exchange as the Najdorf is to the Alapin Sicilian!
SMH!

I always treated the pawn push like the inferior advanced variation. In my head the best thing white can do is to transpose back into the d4 line
All you did here was transpose to the Advance, but here Be3 wasn't an option as d4 hadn't been played yet.
This is why UNDERSTANDING BEATS MEMORIZING. If you understood why 4...Qb6 is better than 4...Nc6 if you are playing both moves anyway after 1.e4 e6 2.d4 d5 3.e5 c5 4.c3, then you wouldn't have questions about alternative move orders. The fact that you question about why one would play Qb6 after 1.e4 e6 2.Nf3?! d5 3.e5 c5 4.c3 just goes to show that you did not pay attention to WHY the move is played first in the first place. If White can't legally play 5.Be3 after his 4th move, then obviously it would make more sense to play 4...Nc6, in case White doesn't play 5.d4, and 5.Be3 is OBVIOUSLY illegal!
Quit getting hung up in names and what-ifs about move order, and actually try to UNDERSTAND why moves are being played. Maybe that means spending 20 minutes at a board figuring out why moves are bad. Books won't tell you every bad move and you cannot just zip through moves at lightning speed and expect to understand jack bleep. Sometimes you have to figure it out for yourself and not expect to be spoonfed, like after 1.e4 e6 2.d4 d5 3.e5 c5 4.c3 Qb6 5.Nf3 Nc6, why the move 6.b3 is so bad!

Nooo, I didn't mean the other variations. I meant something like
Once again, TOTALLY DIFFERENT VARIATION. I will say for the FINAL TIME - in the main line of the Advance French - 1.e4 e6 2.d4 d5 3.e5 c5 4.c3, if you intend to play the 5...Qb6 line, play 4...Qb6 first. THAT LINE - ONLY THAT LINE! You change EVEN ONE MOVE and you have a TOTALLY DIFFERENT POSITION! CAPICHE?
Just because e5 is played doesn't make it the Advance Variation
1.e4 e6 2.d4 d5 3.Nc3 Bb4 4.e5 is not the Advance (Winawer)
1.e4 e6 2.d4 d5 3.Nc3 Nf6 4.e5 is not the Advance (Steinitz)
1.e4 e6 2.Nf3 d5 3.e5 c5 4.b4 is not the Advance (Wing Gambit)
1.e4 e6 2.d4 d5 3.e5 c5 4.Nf3 is not the MAIN LINE of the Advance Variation - Again, THE STRATEGY IS DIFFERENT!
