Like everyone says, the two definitions are equivalent, but if you want an official-looking source, here is the quote from the USCF rulebook:
8E. The knight. The knight’s move is composed of two different steps.
First, it makes one step of one single square along the rank or file
on which it stands. It does not land on that square, as its move is
not complete (9A). Then, still moving away from the square of
departure, it moves one step of one single square on a diagonal. It
does not matter if the square of the first step is occupied.
is sometimes called an L move, as it is equivalent to moving the
knight two squares vertically, then one square horizontally (or two
squares horizontally, then one square vertically). Note that the
knight always moves to a square different in color than that of its
starting square. A knight has a maximum of eight possible moves.
U.S. Chess Federation. United States Chess Federation's Official Rules of Chess, Sixth Edition (Kindle Locations 941-946). Kindle Edition.
There are yet more ways of looking at the knight's move. This one is from the FIDE handbook, and while clearly correct I don't think it reflects the way most people think of the move:
3.6 The knight may move to one of the squares nearest to that on which it
stands but not on the same rank, file or diagonal.