Here are a few key selections from https://pilotinstitute.com/forward-slip-vs-sideslip/
> Both forward and sideslips involve opposite aileron and rudder input. In a forward slip (typically used to increase drag and decrease altitude), the aircraft’s nose points away from the direction of flight, with the lowered wing facing the direction of flight. In a sideslip (typically associated with the final stage of a crosswind landing), the aircraft’s nose points in the direction of flight, regardless of which wing is lowered.
and
> To understand the difference between a forward and a sideslip, we need to understand the slip in general. A slip, at its core, is an uncoordinated turn. In other words, when the ball of the turn coordinator is not in the middle, you’re in a slip.
So in general, a slip is a situation where you're banking, but not turning, due to opposite inputs to ailerons and rudder (i.e. between stick and pedals).
As I read through all that, I thought I was coming to a decent understanding. However, finally,
> The jargon is unnecessarily confusing – you move forward during a forward and a sideslip, but you don’t move sidewards during a sideslip; you technically move sidewards during a forward slip!?
Hmn.