I’ve rescued the Queen from the Cathedral. Now what

In Wait mode if you're in a command menu (i.e. choosing an item or tech to use) time effectively stops. In active mode, Active Time Battle bar is always going; that's the one that fills up and your character can act when it's full. This includes yours and the enemy's which you can't see.

When you're just in the main combat screen and not in a particular menu there is no difference.

Once you learn dual-techs you might actually prefer Active mode, because in Wait mode you would have to sit in the main screen waiting for both characters to be ready to act, whereas in Active mode you can just select the tech while waiting and then just choose it.

That's actually one of the reasons that Wait mode doesn't make it completely "turn-based" the way you expect it to. You sometimes need to wait till 2 characters are ready to act simultaneously and if time stopped when it was 1 character's turn, you wouldn't be able to do so.

Two things you may have forgotten to do:

1. Rescue the Chancellor: he is in the chest on the left hand side of the room in the Boss Fight with Yakra. If you do not rescue him, the cutscene does not play out properly. If you accidentally leave the Chancellor in the chest, he will rescue himself when you leave the room. (That said, you have mentioned that Frog has left, so this might not be the case).
2. Talk to Queen Leene: after the cutscene with Frog, you actually need to talk to Leene, and she will ask "what happened to the girl that was mistaken for me?" Lucca will then react, and ask you to go check out the room where she disappeared from, which should trigger the cutscene where she reappears.

Outside of this, there should be no reason for her not to appear, so it may be a bug in the save file.

As per the comments: the OP found they were going to the wrong room, which is why Marle wasn't appearing.

After talking to the Queen, and Lucca "remembering" about Marle, you will need to enter the doorway to the right at the back of the Throne Room, which will lead to the Queen's Chambers, where you will find Marle (the door to the left leads to the King's Chambers).