So, as far as I can tell, the Rapture predicted by Harold Camping, et al, didn't happy on Saturday. (If it did, then a lot of us are apparently sorely mistaken about the Gospel.) In the wake of the non-event, a noticed a handful of people (on Facebook and Twitter, most notably) questioning whether Camping was a false prophet. Some went so far as to invoke Old Testament requirements (especially from Deuteronomy 18:20) regarding the putting to death of false prophets!
So, was Harold Camping acting in the capacity of prophet? Or was he merely making a prediction? And what's the difference?
Old Testament Prophets
In the most restricted sense of the term, a "prophet" is one who is appointed by the Lord to serve as the one who speaks on behalf of God, often to call God's people into faith and belief, which is usually accompanied by turning from sin and returning to the Lord. Prophecy was often accompanied by the foretelling of future events, always with the goal of advancing this call for belief and return.
One of the earliest prophets so appointed, for example, is Aaron, the brother of Moses: when Moses complained to the Lord about his appointment to lead the people out of Israel, the Lord graciously relented and named Aaron as the one who would speak (Exodus 7:1). Later, Aaron and Miriam (Aaron's sister, who served as a prophetess-- Exodus 15:20) are told by God, "When a prophet of the LORD is among you, I reveal myself to him in visions, I speak to him in dreams" (Numbers 12:6).
In the accounts of prophetic work in the Old Testament, the prophet would often be told to say to the people, "This is what the Lord says" (or in more archaic English, "thus saith the Lord"); that phrase would set apart the words the proceed from the prophet as being one of his specific prophecies, those things which might be tested to be true or untrue. At other times, they are recorded to speak with the authority of God, and while they don't state specific words given to them by the Lord, it is clear that the Lord is Himself behind their words (think of Elijah before the priests of Baal in 1 Kings 18, or Elisha's interactions with Naaman in 2 Kings 6).
New Testament Prophets & Beyond
In the New Testament, we read of John the Baptist as a prophet-- he is often considered to be the last of the "Old Testament" prophets, in that the function that he served was similar to those Old Testament prophets who preached a message to the people of Israel to return to God and prepare for His coming in judgment. Jesus functioned as a prophet also (after all, we ascribe all three offices of Prophet, Priest, and King to Him), foretelling many things about His own death and resurrection, as well as prophesying the coming destruction of Jerusalem and calling Israel to return to the Lord. John the apostle, in the vision recorded in Revelation, was also given prophetic insight into future events, and specific warnings for particular churches.
Other than that, the function of prophecy in the New Testament was more one of verification than of foretelling: prophecy is named as one of the gifts of the Holy Spirit, along with healing, tongues, and interpretation of tongues-- all of which are understood to be means of verifying whether those claiming to be true teachers were actually accompanied by the Holy Spirit in their teaching. Many (myself included) believe that these gifts are no longer given by the Holy Spirit, because we now have a completed Bible by which to verify what the gifts served to verify in the New Testament church.
Even among those who believe that they continue today, to the best of my knowledge (and I confess that I am not well-versed in the teachings of these segments of Christianity), prophecy is not considered to be a source of new words from God in the sense that it was in the Old Testament and, to a more limited extent, in the New Testament. In other words, few or none of these teachers would assert that such prophecies need to be recorded and eventually added into our Bibles. Rather, they are considered either to be a continuing work of verification-- and I am aware that some churches hold to this firmly, even to the point of questioning or rejecting the claims of faith of those who do not demonstrate one or more of these "sign" gifts-- or, perhaps more commonly, to be someone who boldly proclaims the teachings of the existing Word of God as found in the Bible.
Prediction & Harold Camping
For Harold Camping to claim that he knew the precise date of the apocalyptic events (as he did) as a matter of biblical prophecy would be, in essence, to advocate for a new revelation from God. Were this to be the case, then Camping's teachings should either be added to Scripture (if they are true) or he should be ignored and disregarded. Had he lived in Old Testament Israel and the latter been the case, there would have been scriptural merit in calling for his stoning.
But there are plenty of people who make predictions that are not claiming any unique divinely-given inspiration. People predict the weather based on scientific data, the winners of ball games based on statistical information, or how much cash they will need at the grocery store based on their personal experience. If they are off a bit, or completely wrong, they may have consequences: a persistently-inaccurate climatologist will eventually be out of work; a gambler whose statistical analysis regularly leads him to bet on the wrong team will either quit or run out of money; and an under-estimating grocery-shopper may have to put the ice cream and cookies back on the shelf.
Harold Camping's predictions were similarly based: he amassed data and information that he believed led to a particular conclusion regarding what he understood to be the end-times events. But as far as I know, he never stated, "This is what the Lord says," nor even claimed that his insight and predictions were given to him by God.*
There are still consequences: though their website is still boasting that May 21 would be the day of Rapture, I would imagine that many of the listeners and followers of Family Radio International are now skeptics, if not cynics, about the prediction-ability of Camping, et al. Some have reported that Camping has been unavailable for comment since his prediction has been demonstrated inaccurate. I'm sure some regret giving money to support this cause.
But Harold Camping is no prophet, false or otherwise. And to treat him as such is to take his false prediction more seriously than it needs to be.
*Harold Camping, in a booklet distributed on the Family Radio International website (We Are Almost There pdf), implicitly denies that the Scripture is "closed"-- not in the way we typically think of that, in the sense that there are new words and chapters to be added, but by claiming that the ongoing interpretation of the Bible by way of codes, recognition of specific events that are "hidden" in the descriptions of Scripture, etc. are a "third testament" of sorts. While I think this is chicanery that should be condemned, I don't believe it quite qualifies as a claim to "prophetic" insight; even within this framework, there is room for the interpretive conclusions to be wrong.