I'm trying to connect a different Facebook account, but it keeps connecting my personal account
We're really sorry we haven't made this process very clear. If you're already logged into Facebook, when you try to connect an account to Buffer, it will assume that you're looking to connect the account you're logged into. Would you mind logging out of the Facebook account you're currently logged into and then trying to connect the new account through Buffer again? This time it should prompt you to enter the Facebook login details and you'll be able to connect the new account.
If you still have trouble, don't hesitate to get in touch with us and we'd be thrilled to help get things straightened out for you!