Hello-
Recently I have seen some ads for heckel bassoons for sale. They say "pre-war vintage heckel bassoon. great condition. short bore".
What exactly does "short bore mean?"

Long Bore vs. Short Bore
Long-bore models: typically have a warmer tone, even intonation, and are more "stable".

Short-Bore models: have greater flexibility and project better. (supposedly preferred by many orchestral players).

FOX also has a Thick-Wall model which is supposed to combine the most desirable charateristics of both.

You may also look at the type of wood being used; mountain maple, sugar maple, red maple,dark maple.

I think with Heckel, as with most makers, you don't get a choice of wood. Fox are unusual in offering the player a choice of wood.

just curious, would a short bore model look noticeably different from a long bore model?

The difference will only be noticeable by putting two the models side by side.