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Yep, your hitbox for taking damage only includes the center bit, not the wings; however your hitbox for collection does include your wings.  This is intended to skew advantage to the player, but i can see how it can be a tad confusing.  Also protip: your plane can fire at an angle; notice how your plane turns when moving.  If you get into a situation where there are too many enemies in a certain part of the screen, you don't actually have to move in front of them to clear them.  Try holding a direction key and tapping the fire button when your aiming laser is on top of enemies, then holding the opposite direction before you get too close.