A narcissist is what someone is, but being a self-centered person is something that someone does. It is expected that a narcissist is arrogant and selfish. However, being self-obsessed means they might not be obsessed with themselves, they are just making choices at the moment that are driven by stress or ignorance.
This behavior doesn't mean that they are fundamentally self-focused and self-obsessed like a true narcissist. Many narcissists are quite socially integrated and fit in with many social groups. People who are self-obsessed may not be as socially accepted because of how they appear to others.