This is a type of puzzle that at first looks like a tile-sliding puzzle, where you have a grid of tiles with 1 missing tile, and you can slide individual tiles into the blank spot, eventually arranging them in the right order.
But it's quite different -- there is no blank spot, and you slide an entire row or column of tiles at a time, where the title that overflows wraps around to the other side. It seems to have more in common with a Rubik's Cube than a sliding puzzle.
Here's an example: https://www.proprofs.com/games/row-slide-puzzle/
There is also an Apple Arcade game The Enchanted World (trailer) with these types of puzzles -- only they aren't in perfect square shapes, each row can have a different number of tiles, and there is sometimes move count limitations, or a mobile bad guy that makes titles unmovable. What makes its puzzles more challenging is that half the puzzle is figuring out what the correct arrangement even is -- as if getting into that arrangement wasn't a challenge enough :)
I can't seem to find any information about solutions to these types of puzzles. All the information I find is about tile sliding puzzles, and Rubik's Cube type puzzles are more complex. This is like a 2D rubik's cube.
Is there a name for this type of puzzle? What movement techniques are useful for solving them?
For example, one technique I've identified lets you fix the order of titles in a particular row. Say the row is '1324' and you need it to be '1234'. This is really 2 separate steps -- the 2 and 3 are each in the wrong position, and you can fix each one separately. For the 2, slide its column up or down, separating it from the row. Then slide the row such that the position the 2 should be in is adjacent to the 2, then slide 2's column the opposite way as you originally did, and now 2 is in the correct position (and if necessary you may now slide the row back to how it originally was relative to the rest of the puzzle). Repeat for 3. The issue with this technique is that it does not leave the rest of the board as it was. You invariably end up trading one misplaced tile for another, just moving the problem around. Insights or academic links to similar puzzles would be helpful!