Joy and Elsa have a heart-shaped face: wider at the top, with a pointed chin, and a point of hair that sticks down in the center of the forehead. Disgust and Merida have round faces. Sadness has a pear shape, wider at the bottom than at the top, pretty rare. Vanellope has a square face, look how flat it is on the bottom.
If you are an artist or a writer, you can avoid the cookie cutter effect by thinking about infrastructure. One way to do this is to use reference photos. I've been working my way through a splendid lineup of Olympic athletes. When writing outside your own race/culture, using a sample photo -- especially of someone who seems "like" your character in some ways -- can help create a look that is well put-together and makes sense. Another option is to make model sheets, like these from classic Elfquest. This is ideal if you're creating a batch of characters all together, like the members of a team: you want them to contrast so they're easy to tell apart. When designing a character, you may consult charts of body shape (male and female), face shape, eyes, ears, noses and lips. Understand that certain features appear more or less often based on ethnic group, but populations have mingled a lot, so don't be afraid to mix and match. Also for nonbinary sex/gender identity, either minimize strong sexual clues (very long or very short hair, pronounced angular or curved lines) or combine ones from both polarities.