Yes, the term has become quite loaded. However, I disagree with Potemkin_Prod's interpretation.
No matter how good Exeter, Intrepid, Star Trek Continues, Axanar or Phase II or any of the fan films are, to my mind, they are still fan-produced projects simply because they are not the copyright holders of the intellectual property they are producing nor are they doing so with the express intent of said owners.
They're still just a bunch of fans making a movie. And that's great. That's wonderful and special. It takes a lot to achieve something like that and I applaud each group for doing so every time they do for this very reason. How many fan films have we seen announced over the years that wither away into the ether?
One of my personal frustrations with the Phase II productions has been the consistent lack of original content produced by the Cawley Entertainment Group. They certainly have the resources. Phase II is clearly their bread and butter but their forays into the now all but disowned Buck Rogers Begins and the supposedly upcoming Wild Wild West fan films betray a real lack of desire to venture into their own original productions while at the same time insisting (and at times demanding) that they be taken seriously as a "professional" production.
Contrast this with some of the personnel from Exeter, who went on to produce "Polaris," an original film. Or Intrepid, whose production team is likewise branching out to produce original content with Wicked Things, an intended original series. Even Rob Caves tried to break away from his Hidden Frontier empire and create something new and original with the short-lived Frontier Guard.
Obviously, neither way is right or wrong, nor more "right" than the other, but it's hard not to look at these two disparate groups and see one basically trading sandboxes in order to continue to play dressup while the others strive to create something new and original. And all my criticisms of Phase II aside, I think the biggest issue for me is that they so often are like Icarus, reaching for the sun and almost getting there before something comes along and melts their wings. They have the capability to do something really special. We've seen it already with what is easily their finest offering, "World Enough And Time," but they just don't seem to want to make that push forward.
In short: in my own opinion anything with the name Star Trek on it that wasn't commissioned and produced by CBS or Paramount is still a fan film. You can land celebrity guest stars, you can get pros to write and produce your shows, but in the end, they're all just vanity projects, not tied to the actual literary, televised, or official canon of the intellectual property.
Note: this certainly does not preclude, however, that some of these films are still superb hours of entertainment. Star Trek Continues' "Lolani" was especially well done; "World Enough and Time" is a classic, and Exeter's "The Tressaurian Intersection" I think is the finest example of being it's own film while also being one of the best fan films I've ever seen.