when they redid the T3, 7th floor (club level) with a large suite some years back, they lost the 2 king suites that had the pool view.
i book king suite each year.
a floor lower and get the pool/park view.
to me, the view is a priority than staying on club level.
club level is at tower 3.
there at time periods that you can add club to your reservation if you are not staying on floor 7.
probably $100 per night for that addition of club.
if you are looking for available rooms on the booking website, if king club or king suite is not listed, that would mean none are available for your dates you listed.
king room means king bed.
king suite is the two rooms
king club means a king bed on club floor.