The key, I think, is to try to distinguish the Protagonist from the MC in your mind. Let's call Woody "The Cowboy" when we're looking at him as a Protagonist.
The Cowboy is the leader of all of Andy's toys. His problem arises from the Situation he finds himself in: accidentally abandoned by his owner with the Space Ranger. The Cowboy's Goal is to make it back to Andy's house safe and sound, but he can't do it alone. He'll need the Space Ranger's help to leave the gas station, escape Sid's house of terror, and make it back before Andy loses them both for good.
Woody is the Main Character. Upon the introduction of Buzz Lightyear, he begins to struggle with the notion that he's not the top toy anymore. This struggle comes through in what he does; specifically, his tendency to jump the gun and take the lead on Activities. Sometimes this gets him into trouble, like when he accidentally knocks Buzz out the window; other times, he's invaluable, like when he pilots the remote car back home.
Perhaps you can imagine an alternate version of these two characters where Woody is a Be-er instead of a Do-er. The first story as the Cowboy would be exactly the same: the Protagonist pushes the other characters to complete the Goal. But as a Be-er instead of a Do-er, Woody would solve his problems through persuasion and belief rather than through activities.
Another thing you can do is note that Woody's Critical Element, Determination, is actually a Contagonist Element, not a Protagonist Element. So while the Cowboy leads the toys Protagonistically, Woody struggles with Contagonistic forces inside himself. This Complex interaction leads to some of the conflicts in the story, like when he knocks Buzz out the window, Hindering any chance of creating peace in the household.
Does that make any sense?
Fake Edit: For some reason, I thought the storyform was very different, with Woody being a Steadfast character. In either case, the explanation should still hold.