So in order to log into most websites, you need your username/email address and a password.
You can save your username/password in your web browser or in the cloud.
Sometimes people get lazy and reuse passwords, sometimes people forget their passwords.
Passkey is a replacement for usernames/passwords. It does require that the passkey is saved somewhere, often on your device (in the cloud is possible, but non-standard).
When you "create" a passkey, this passkey is used only at a single place. For example, you'd have a passkey for your bank, another one for your email, another one for Lemmy. You have no say in the matter, that's just how it works.
When you log into a website that has passkey enabled, your passkey/password manager pops up, you click on the passkey and that's it. There is no email address, there is no password, no MFA.
edit: oh, you also asked about the difference between passwords.
It's all about improved security.
You go to certain websites, and they'll only allow a-zA-Z0-9, others require a minimum length of 8 characters, needs 3 symbols (except ! for whatever reason ;)
Then you have no idea how the website is storing your password. Are they encrypting it? Did they do it correctly?
If you look at the number of "breached/leaked" passwords on the internet, it's because it's hard to securely store passwords.
Passkey solves all this. Websites are just given "a public key" and it can be "just stored", no special treatment necessary.