To be self-centered is to be selfish, to only worry about how things affect you. To behave in the way that benefits you.
To be full of yourself is to have a very high estimation of your own abilities and worth.
They are not the same thing, but are often found together.
The opposite of a self-centered person is someone who is caring and altruistic.
The opposite of someone who is full of himself is a humble person.
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