i think they might be the same thing? gates aren't really brought up as much throughout the story but i've always assumed they were a type of rift. they distinguish the two in the korean version too.
theyre interchangeable, however the difference between rifts and dungeons are that rifts pull in the surrounding area and need to be closed meanwhile dungeons just need to be regulated and are used to farm items (ofc in the past they were closed too due to lack of manpower)
OMG THE MOMENT IVE BEEN WAITING FORRRRRR