Slide Puzzles. Jigsaw Puzzles.
You see, the differences between Slide Puzzles and Jigsaw Puzzles are interesting.
The solving of a Jigsaw Puzzle often begins with the classic "corner pieces first, since they're easily identifiable by shape" technique. This technique does not really apply to a Slide Puzzle, though. Slide Puzzles tiles are all, by necessity, identically shaped, and thus cannot be differentiated in that way—If the corner piece of a Slide Puzzle is to be differentiated then it will be by the design; many Slide Puzzles designs feature a border around the edges, which produces visually differentiated corner pieces equivalent to the physically differentiated corner piece in a Jigsaw Puzzle. Oftentimes, this does not even matter; The corner-piece-technique is not even particularly relevant with a Slide Puzzle as it would be with a Jigsaw Puzzle due to the difference in their mechanics.
The main challenge of a Slide Puzzle does not lie in identifying where each piece must go to form a complete image—identifying which piece connects to which—as it does with a Jigsaw Puzzle. Instead, I would argue the main challenge of a Slide Puzzle lies more in the mechanics of sliding the tiles to where you want them to go. Trying to identify the intended placement of a tile is secondary, hence their simpler designs and vastly lower piece-counts compared to Jigsaw Puzzles. The challenge is their interconnected movements.
With a Jigsaw Puzzle, all pieces can be placed and removed freely. Connecting a piece once its place has been identified is trivial. On the other hand, with a Slide Puzzle, each piece is always connected and always must remain connected. You cannot move one tile without also moving another which touches it, and another which touches that, so on and so forth. To allow any movement in the first place, there is always a missing or displaceable tile to create an empty space, usually in one of the 4 corners.
The safest way to solve a Slide Puzzle is by beginning with the sides opposite to that empty space. For example, if the empty space is in the bottom right corner, then the uppermost row and leftmost column should be arranged into proper order first, then move on to the next row and column once closer to the empty space, then next row and column closer, so on and so forth until the puzzle is fully solved.
That is just the safest and most consistent way to solve it, though. It can be solved in other ways, the most intuitive of which is to simply sort row by row, starting furthest from the empty space. If you do that, though, you run the risk of ending up with a large majority solved, but the very last row stuck in improper order.
A classic "1, 2, 3, 4—5, 6, 7, 8—9, 10, 11, 12—14, 15, 13" situation.
And a Slide Puzzle is always connected in sequence. A tile cannot be moved individually and always must disturb those around it to change its own place. This can be daunting at first—you may wish you could simply pick out that "13" and put it before the "14, 15," so as to not disturb the rest of the puzzle which has already been "solved." But, of course, it is not really solved. The tiles are not individual, they are each connected; regardless of how they may look, if one tile in the final row is out of place, then the rest are out of place, too. Something has gone wrong somewhere in the process.
To right it and arrive at a solved puzzle, you cannot be afraid to rearrange it all. Because no tile can be changed in isolation, you'll need to pull the rest from their current sequence into seeming disarray—but because no tile can be changed in isolation, it is impossible to rearrange in a way that makes it unfixable. This is just the process of change. It was in order once and can be put in order again; thus, you must trust, despite the disturbance that occurs to the rest of the tiles to put the last row in order, that everything will fall into place once more. Because it will.
"1, 2, 3, 4—5, 6, 7, 8—9, 10, 11, 12—14, 15, 13"
"1, 2, 3, 4—5, 6, 7, 8—9, 10, 11, 13—14, 12, 15"
"1, 2, 3, 4—5, 6, 7, 8—9, 10, 15, 12—13, 11, 14"
"1, 2, 3, 4—5, 6, 7, 8—9, 10, 11, 12—13, 14, 15"