Cling/skid is very different from throw. They are the same kind of effect but skid is much larger probably due to chalk at the contact point.
The only way for the cue ball to send the object ball other than along the ideal line of centers (cue ball to object ball line at the instant of contact), is for the surface of the cue ball to rub sideways on the object ball. That has two effects. The first is throw (or skid, if the contact is bad). The second is that the object ball will have side spin. More throw, more sidespin. The same force that angles the object ball off-line will put side spin on it.