Skill vs. Luck - Another Angle

[OldNantucker]

Sports Analogy: Mighty Patriots play lowly Lions and final score is 24-20 Lions. Pats had 380 yds of total offense and Lions had 165. Lions get two TD's when two passes are randomly deflected, intercepted and run back for TD's.
Pats are clearly more "skilled" team who made better plays but lost the game due to unlucky breaks. Obviously, football is a game of skill but some games have an element of luck.

I play Phil Ivey heads up and he skillfully manuevers me into playing big pots after flop as 2:1 and sometimes 4:1 dog. I get lucky, draw out and eventually bust him. Clearly, Ivey is the more "skilled" player who has put the odds in his favor by making better plays but was unlucky. Poker is a game of skill but many times has an element of luck.

Aren't these examples the same thing? Don't many skill games have an element of luck?