1. As the name “prophet” suggests, prophesying will be the dominant feature of a prophet’s ministry. To prophesy simply means to speak forth a revelation we have personally received from God (the Greek word literally means to “speak forth”). Whereas all believers can prophesy, prophecy will not necessarily be the dominant feature of that believer’s ministry (e.g. a teacher may prophesy from time to time, but his or her ministry will be dominated by teaching). But if they are a prophet, his or her ministry will be dominated by the prophetic! Prophets are continuously speaking forth revelations that they have received from God (e.g. Acts 11:27-28).
2. The office of prophet is one of the leadership offices in the body of Christ that exists to “equip the saints for the work of the ministry” (Ephesians 4:11-12). Not all believers are called to such a leadership office, but the prophet is.
3. As the office of prophet is a leadership role, I would expect that a resident prophet would usually be one of the preachers in his or her local church (just my opinion based on the logic of my second point above, and my reading of Acts 15:32 where the role of preaching seems to be implied in Judas and Silas’ designation as “prophets”; but notice my word “usually” as opposed to “always” - we can't put God in a box). Not all believers are called to be preachers.
So, those are three distinctions: their ministry is dominated by the prophetic, the office is a leadership office in the body of Christ, and theirs is often a preaching ministry. The same cannot be said of all believers (all of whom can prophesy). But if that it is still not clear, perhaps the following analogy will be useful: we can all cook (I hope!), but that doesn’t mean we are all chefs! Similarly, we can all evangelize, but that doesn’t mean we all occupy the office of an evangelist. There is a sense in which we are all “sent”, but we do not all occupy the office of apostle (“apostle” is literally “sent one” in the Greek). We can all teach one another, but we do not all occupy the office of teacher. Even so, we can all prophesy, but we are not all prophets (see 1 Corinthians 12:29 and Ephesians 4:11 on this point).
To find out how you can move in the prophetic, click here to read my blog post about how to prophesy.