Beyond just what they stand for (which, to me isn't really all that different), there are some inherent construction differences between the two. At least if comparing an average mascot costume to a fursuit.
Mascot costumes are built to take a beating. You pretty much expect that the wearer won't take the same level of care of the mascot costume as what somebody would do with a fursuit. Also, mascot costumes tend to be one-size-fits-all, so the body would probably be fairly baggy (if it has one).
On top of all that, particularly with team mascots for larger sports teams, the style and proportions of the characters tend to be vastly different. Everything is even more exaggerated. For example, a lot of mascots will have very large heads. These are actually sometimes shoulder-mounted, so if the performer wants to turn the characters head, they have to actually turn with their whole upper body. Fursuit masks are typically fitted to the head of the wearer, so simply turning your own head will turn the characer's head. I think a big reason they use the proportions that they do is for visibility. In even a medium-sized stadium, it's much easier to be able to tell what the character is from anywhere in the stadium when they use the larger style head/features.
