Mentsch1 the terms I have used are based on the Rambam s definition in the last two prakim of hilchos melachim (and no one is cholek on the Rambam) where the Rambam halachically defines who can be considered a suitable candidate to be moshiach (bchezkas moshiach) and the second stage of moshiach vadai- someone we certainly know to be moshiach (because he builds the BHMK etc) from the fact that the Rambam defines this halachically indicates that we should be on the lookout to identify moshiach using these criteria.
There have been piskei din to this effect as well
Anyhow fascinating topic…