Fork vs skewer: two targets, two different geometries
Both win material by attacking two things at once. They are told apart by whether the two targets are on the same line.
The difference in one sentence
A fork attacks two or more pieces in different directions from one square. A skewer attacks two pieces that stand on the same line, one behind the other, so the attack passes through the front one to reach the back one.
The tell is geometric and instant. If you can draw a single straight line through both targets and the attacking piece, it is a skewer, or a pin if the value order is reversed. If the targets are in two different directions, it is a fork.
The pieces that can do each differ too. Any piece can fork, including a pawn and the king, because a fork only needs one square that attacks two others. Only bishops, rooks and queens can skewer, because a skewer needs a line.
In practice forks are the more common of the two by a wide margin, particularly knight forks, and skewers become more frequent as pieces come off and lines open. If you are studying one of them first, study forks.
One of each
Forks
Position 1
Black to move. Find the best move.
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27.Rxd5 27...Ne3+ 28.Kc1 28...Nxd5
The line wins a rook. One piece attacks two targets in different directions, so only one of them can be saved.
The position comes from an endgame of a real game, rated 587 for difficulty. The answer reaches a winning advantage.
Skewers
Position 2
Black to move. Find the best move.
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40.f5 40...Rxg2+ 41.Kf4 41...Rxg7
The line wins a rook. The two targets are on one line, and the piece in front must move out of the way of the piece behind it.
The position comes from an endgame of a real game, rated 610 for difficulty. The answer reaches a winning advantage.
Questions people ask
What is the difference between a fork and a skewer?
A fork attacks two pieces in different directions from a single square. A skewer attacks two pieces on the same line, hitting the front one so that moving it exposes the one behind.
Can a knight skewer?
No. A knight can fork -- it is the best forking piece in chess -- but a skewer requires an attack along a rank, file or diagonal, which a knight does not have.
Which happens more often in real games?
Forks, by a large margin, especially knight forks in the middlegame. Skewers become relatively more common in endgames, where open lines and few pieces make alignments frequent.