Those two things are not the same thing at all. For example, let's say I want to create new account in your application and you ask me to enter u/p. I enter the

Those two things are not the same thing at all. For example, let's say I want to create new account in your application and you ask me to enter u/p. I enter the string that is already used by another user, so I should choose another one. Except, now I can login with another's person u/p combo. I don't see any reason why you should do a single string login.