Neither one. Severely dislike both. Abbreviations are a sloppy choice, more often than not. I have one relative who abuses them in conversation. She sounds like a nutcase.
I still don't know how, when or why these abbreviations began. When I left for USC there literally was no such thing as Fins. If you watch the clips from the '70s you won't hear that reference. Nor into the early 1980s. Occasionally someone would think it was cute to say Fish. I remember Rick Weaver being annoyed and emphasizing that a dolphin is not a fish. When I returned to Miami at Christmas I began to hear the term Fins in small doses but I never thought it would take hold.
Now, if Mike Dee were involved at that point, I would have understood, and predicted. He butchers everything.
That new thing on the helmet, the motion sickness logo staring blankly upward to demonstrate he doesn't remotely care about you, that qualifies as a Fin.
I also wouldn't doubt that the stadium had something to do with the bland abbreviation. This probably dates to 1987.
These days the one classy member of the organization is John Congemi, who always says Dolphins and normally allows the full version...Miami Dolphins.