What's the physicochemical difference between a chromophore and a fluorophore?
The physical chemistry of fluorescence is a little bit complicated, and so you should consult a text book for "the reason" that things fluoresce.

One of the things that I have noticed is that fluorescent compounds often have several "heavy halogens" Br and I attached to some poly-aromatic hydrocarbon.

Disclaimer: this is not to say that the halogens are the fluorescing portion of the molecule (it's probably almost the whole molecule, conjugation + halogen), and it does not mean that all compounds that contain Br and I will be fluorescent. It also does not mean that Br and I are required for fluorescence.

I think that a lot of fluorescent molecules were discovered by chance, or even brute-force changing substituents until the molecule exhibits the desired fluorescence.  (It's really too hard to predict with qualitative theory, and electronic structure theory descriptions of fluorescence are also very difficult.)