Distortion through a smartphone lens is down to focal length. The human eye sees approximately with the equivalent of a focal length of about 50mm (this is just a rule of thumb as human vision is variable and doesn’t work like a lense-sensor-setup). Standard smartphone cameras usually have a shorter focal length which leads to more distortion. Your front camera might have a fl closer to 50, but here I’m just guessing.
There’s also the issue of your face being mirrored, ie flipped, in a mirror and your Selfie cam. This is not actually distortion, though.
It’s because in a mirror and on your front camera your image is flipped (mirrored) and so when you see yourself in a normal picture / back camera it may be jarring because you’re not used to seeing that version of your face. To everyone else who has always known you, this is what you’ve always looked like, but your mind has a slightly different face that it sees in the mirror every morning and when you open your front camera
Back when front selfie cams became a thing on smartphones, in the beginning it was just another camera added there. That freaked people out because it felt like looking in a mirror, but the image wasn’t mirrored. So it looked subtly wrong to people and they had a hard time pointing out why. Mirroring the image fixed it. Depending on what phone you have, it should be pretty trivial to mirror a picture, try that and see if it still looks “distorted”.
Taking pictures from close up with a wide angle lens gives a distorted perspective, with your nose looking bigger and your face rounder. You don’t usually look at people that close by eye so it looks unnatural and unattractive. That’s why photographers usually use a lens with a longer-than-standard focal length for portraits, i.e., they have the subject stand away from the camera and use a lens with a slightly narrower field of view.
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