The key difference is that during normal use, the private key of the passkey doesn’t leave the device (or password manager). The passkey basically comes in 2 parts, the public and private (secret) part. In order to log in, the website presents a cryptographic challenge that is only solvable using your private key - and crucially you can solve the challenge without revealing your private key. An attacker could get your answer to the challenge and still be unable to solve additional challenges without the private part of your passkey.

This of course makes it basically impossible to manually log in using a passkey and a keyboard, without any password manager to do the cryptographic calculations (unless you have a LOT of paper and time), but the security advantage of making it near impossible to be phished is generally regarded as a net positive. In order to steal a passkey there would need to be a vulnerability in the software, since passkeys make it much harder to trick a user into giving it away (since tricking the user into logging in on a fake website doesn’t work due to the aforementioned cryptography, the main way to steal a passkey would be to trick the user into exporting it - which is a much higher bar).