Front facing vs rear facing camera difference?

When I take a picture with my iphone, when I do a front facing camera or a rear facing from the iphone camera app, my face looks distorted.

heres an example:
front faced
rear faced

But when I take a selfie on snapchat my face looks normal:
image

Which is supposed to be a more accurate representation?

They all look fine. The issue is how far away you hold the camera. The closer you hold it, the more distortion you are going to get, because with wide-ish lenses, you get more distortion at the edges of the frame.

Notice in the first and last pictures your nose is bigger and your ears are more hidden (I'm not sure why you think the 3rd one is better other than color which is a matter of lighting) and this is because the camera is closer to your face (and your nose) and your cheeks block part of your ears when closer. The middle one is probably fairer as to what people see standing that distance from you.

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