Is a slip an intentional consequence of a cross-control?
You are right: A slip is a cross-controlled (and uncoordinated) situation. It's exactly what your instructor was teaching you to avoid during your early lessons.

As far as nomenclature goes: all slips are cross-controlled maneuvers, but not all cross-controlled maneuvers are slips: On climb-out in most piston singles you will be stomping on the right rudder to offset the plane's left-turning tendencies, and you will probably notice that you're rolling in a tiny bit of left aileron (which offsets the banking tendency introduced by the rudder) - your controls may be very slightly crossed, but the result is coordinated flight (a centered ball).



The real difference here between an "unintentionally cross-controlled situation" and an "intentional slip" is the intentional bit: When you are knowingly slipping the aircraft - for example to bleed off altitude on a high final without increasing your airspeed - you're aware that you're flying in an uncoordinated and aerodynamically unstable condition. You're aware of the risks, and are hopefully monitoring the aircraft carefully to avoid a stall/spin.

For a little more insight, faaflighttest.us has a reprint/copy of an Aviation Safety article from April 2006 which is worth a read, and possibly an hour in the air practicing some of what they discuss with your instructor so you can get the "feel".