It depends on the film.
And it's certainly very rare these days, but in the past almost all films were shot in academy ratio. So they would all be full frame.
We also use full frame when a film is shot in academy ratio, and projected cropped in the cinema (Stanley Kubrick did this a lot).
If you don't know for sure that a film is pan & scan or full frame, go with what's on the cover until you know which one is right.
Aspect ratio is very complicated, and very difficult to explain in words, but if you have any other questions I'm sure we'll try and answer them.

Most 1.85, 1.78 and 1.66 ratio films in 1.33 are open matte, although there are excpetions like "King Of New York" and "Hard Boiled" which were "hard-matted" to 1.85. Hard mattes mean the theater projection isn't doing the matting like on most, the matte is on the film frames. This makes the 1.33 versions pan and scan as the extra picture info is gone and can't be used. I read something about this being an expensive process which is why it's pretty rare to see and over 90% of 1.85 films are open matte FF when shown 1.33.
If a disc has both versions compare a couple scenes. If there's extra picture on the top and bottom it's open matte, which equals Full Frame. If there's no extra on the top and/or bottom and lots missing from the sides, then it's P&S.

This is a good place to start. Maybe someday I'll feel brave enough to try and explain the 2.35 ratio films which were shot with super-35.    

Screw it, I'll try quickly.
Super-35 gives the option of opening up mattes but usually ends up being something else, a cross of FF and P&S. If you have the T2 Ultimate edition, there's a great demo in the supplements showing a scene being transfered for home video. Look under "home video" or "transfering to video", something like that. Haven't watched in a while but it taught me more in 5 minutes than hours of web surfing did. Bottom line is it's all over the place. A few seconds might be the whole frame, then a couple seconds later it's zoomed in tight enough to cut picture from all 4 sides. The 1.33 box is constantly moving and chaging size all around the frame to include whatever the monkey doing the tranfer considers the "most important part of the picture". Casino suffered from this as well. If you still have a 1.33 VHS, compare that to the WS dvd. The Matrix movies are also Super-35.

One last tip on spotting Super-35. If the open and end credits are WS, the movie is NOT S-35 and is Panavision, which means it's all P&S. End credits are the best tell as they sometimes will open up the opening credits or put the words in different sizes and spots on the frame. If the end credits go to WS, it's definitly P&S. If they don't, then the matte has just been opened up and it's Super-35.
Also on long shots, anamorphic film (like Panavision) will make straight lines bend inward near the sides on longer shots. I can't think of a perfect example right now but have seen it in most John Carpenter films, esp. in Prince of Darkness (not a great example as it's not a huge movie many will have). There's a long shot down the street and the light posts on the edge of the frame are bending inward big time. Most examples are more subtitle but if you're looking for it you can see it easily.

As someone who voted no on one of your submissions then switched to yes after a PM, I can tell you that you're getting no's partly b/c you're not giving a source for your claims.  The one I voted on just said you were changing it b/c of the rules.  No reason was given for how you proved that that case was wrong.  It turned out you had 2 programs that you were able to verify that the movie was p&s vs full frame and I voted yes once you changed your contrib notes to reflect this.

For any change to a profile, you must submit your sources, be it the dvd, the cover or an outside source.

This explanation of anamorphic format is also worth reading when considering modern films