Notice how it does not say through belief in Christ?
I don't see that having faith in something and believing in something are different. There's certainly no difference in the original Greek in the verse you're quoting. Faith or belief is totally up to the translator. In the KJV, the noun pistis is translated faith and the verb pisteo is translated believe. No difference.
If you want to differentiate the terms, you can specify what you mean by each of them, and I'll use your definitions in understanding what you are saying to me. When you tell me that a verse in the Bible differentiates the terms, it's just not true. The Greeks have pistis only. When it's a verb, then there's peitho, which is sometimes tranlated obey and sometimes believe, and pisteo, always believe, but as a noun, there's just pistis. Only English speakers can differentiate faith and belief, you can't put that in the Bible.