Yes believing in Christ and being saved go together of course. It is only through belief in Christ that we are saved. In the KJV of Ephesians 1:13, it uses the word after, which to me does make kind of a big difference. After we believe in Christ, then Christ grants us salvation. I'm not saying there has to necessarily be a lapse in time between these two things; I'm just saying they are two distinct things, as opposed to one and the same. See my response to Rainy below, that is kind of a summation of what I am saying here.