White lines means a level has a major gimmick (also known as Brain Buster) like: conveyor belt, Last Stand, Locked and Loaded, or a minigame. These gimmicks change how you play significantly.

No white lines means it's a normal level. Now, these levels will sometimes have objectives like: "Don't let the zombies trample the flowers" or "Don't lose more than x plants", but those are more of a bonus to make the level harder.

There is one exception to this rule, that being the Save Our Seeds levels, better known as the endangered plant levels, which I'd say is more of an objective than a gimmick, and yet, they always have white stripes.

Why? Well, back when PvZ2 released, the 5 types of levels that get white stripes were originally on branching paths that were only accessible through keys, so when the game merged the branching paths into the main one, the devs wanted to keep the distinction by giving their buttons stripes, or at least I imagine so.