People use the terms differently.
To me, flameout hops are added immediately as heat is cut, and the wort chilled immediately as a whole (as in either an immersion chiller or a recirced heatex or CFC).
Whirlpool hops are added shortly after heat is cut, while still barely sub-boil, and allowed to steep while the wort is spun and allowed to settle.
Hopstand hops are added after the wort has already been chilled to a specific temp (for me, usually 180F or lower, below the range where alpha acids isomerize or at least significantly isomerize) and held there for a length of time.
Now, while "whirlpool hops" means something specific to me, both "flameout" and "hop stand" could include the rotation of a physical whirlpool depending on your equipment configuration (if you recirc through an external chiller and whirlpool arm back into the kettle, or even just a pump/manual stirring in conjunction with an immersion chiller).
They will impact your wort differently.
Flameout hops and hopstand hops often add minimal bitterness (depending on how quickly it's chilled or what temp the hopstand is at) due to minimal or no time in isomerization ranges, but whirlpool hops can add significant bitterness as alphas continue to isomerize during a hot whirlpool
I configure hop schedules very differently depending on how I'm set up. I normally do whirlpool hops due to equipment concerns, and I typically add no late-boil hops, only bittering and then whirlpool (and perhaps at stages DURING whirlpool). If I'm able to chill the whole batch in the kettle, then I might use a combo of late boil, flameout, AND hopstand.
Again, that's how *I* use the terms. The language people use can change but the underlying processes and implications shouldn't change too much.