Will adding a second ‘account’ under the same seed/pin in LL give it a different public key?

I am a bit concerned with the interpretation of the 'First In First Out' principle in my Satoshi stack.

One interpretation could be, that an output of a designated second wallet does not affect the old stash.
So I am wondering:
Will adding another account '2' give me a another public key for this account and will anyone or any ageny that knows my xPub be able to link it to my old account '1'?

Adding a (temporary)'passphrase is not an option here.

Account 1 will remain untouched.

Thanks for yout help!