Hand rankings are based on the odds of getting each hand. Those odds are based on 5 cards, not 6 or 7. Since hold'em is really mutated 7-card stud, and 7-card stud is really mutated 5-card stud, they all use the same hand rankings.

Your goal is to make the best 5-card hand, so when you hold A7 and the board is A2266, your best hand is AA667, and any better A beats you. If the board was A226K, your hand is AA22K, and the only aces that beat you are A2, A6, and AK.