Summary:

Out-to-in swing: Club hits the ball while moving from the ball's right side to the ball's left side. This puts spin on the ball causing the front to rotate around some on the right side. This causes the ball to curve right.

In-to-out swing: Club hits the ball while moving from the ball's left side to the ball's right side. This puts spin on the ball causing the front to rotate around some on the left side. This causes the ball to curve left.

Remember, the direction the clubface points is the direction the ball starts. The path of the club relative to the clubface dictates the spin on the ball, which in turn dictates how the ball will travel in the air.

The best way (I think) to think of the swing path as being defined by either the clubface at impact or or the target line, depending on which is of interest to you. As far as the ball flight laws go the clubface is the only one that matters, but since we do have mental targets and don't always execute the swing we wanted to, it helps to think of the target line sometimes.

So, assuming your body is properly aligned with your target (and remembering the definitions of different ball flights):
* If the clubface was open (pointed right of the target) and you swing straight at the target, your swing path was "out-to-in" relative to the face, and you'll hit a fade.
* If the clubface was closed (pointed left of the target) and you swing straight at the target, your swing path was "in-to-out" relative to the face, and you'll hit a draw.
* If the clubface was open to the target and you swing straight relative to the clubface, your swing path was straight relative to the face and in-to-out relative to the target line. You will hit a simple push.
* If the clubface is slightly open to the target and you swing even more open to the target, your swing path was in-to-out relative to both the clubface and the target line. Because it was in-to-out relative to the clubface, you will hit a draw even though the clubface was open relative to the target line.

Now, most golfers, practically all high handicappers and probably most mid-handicappers, try to get the clubface square to the target at impact, or very near square, so you usually hear people discuss a swing path with the assumption that the clubface is pointed down the target line. So you will hear things such as "an out-to-in swing relative to the target line causes a slice", which you know now is not fully true because it depends on where the clubface was pointed. But most people assume the clubface is very closely aligned with the target line so they omit that information.

So... coming back to the original question, an a hook is caused by in-to-out swing, a slice is caused by an out-to-in swing, and if you are getting the clubface square to the target at impact (which most people manage to do most of the time), then the in-out vs out-in swings are very different.