The difference is that when you really believe somehting, your internal predictive model of reality contains it, which would mean you sometimes predict different results and act accordingly.

Externally, I don't know, but it sure feels different. Also, there's a partial-believing state that I was in for years as a child and teenager, where I didn't really believe (and hence didn't pray except to show belief in public), but I still kinda believed (and hence was afraid that God would punish me for sinning). At the same time.