Hindering terrain is one of those things that has strict or loose definitions, depending on whom you ask.
By a strict definition? Hindering terrain is whatever the GM marked as hindering terrain on the map (and nothing that's been laid down unless it was a terrain modification that added "hindering" or the lot to it).
By a loose definition, it's anything that damages/attacks the target just for entering it (but not "challenging terrain", which requires a roll). So walls, traps, and pits would all count as "hindering terrain" even if they were laid down by the party -- but zones and other things that did damage when a character started their turn next to/in them would not, any more than being forced next to a fighter with Rain of Steel or a Stormwarden would count as "hindering terrain."
And yeah, if something tries to force you into hindering terrain, you can make a save and drop prone instead of moving if you make it (or just not move, if it's teleportation).