Mined Coins

Can we clarify: Am I correct in assuming that it does not matter what coin each person mines individually as the "pool" pays for the work, not the individual miner. We are essentially socializing the payments based on submitted hash rates? (I have seen a few answers to this)

Essentially.... the program picks the best coin for your machine. Absent issues with rejected shares, you are not rewarded or penalized for the individual coin. ??