As a liberal, I don't entirely agree with Biden. I especially disagree with his foreign policy. I think the difference between liberals and leftists, as you put it, appears to be:

1) Liberals understand the complexity of the system and that the leader does not hold all the power;

2) Liberals are much more skeptical about power, we want nobody to be able to wield it against others, except in an equal way that equally benefits everyone, and that is widely accepted across society.

The second point is especially important.