Both techniques are basically forms of the same thing, size exclusion chromatography (SEC), where molecules are differentiated by size on the basis of their ability to penetrate porous materials. I think the difference is mainly historical; GFC was developed by biochemists to separate biochemical molecules like proteins; GPC was developed by polymer chemists to analyse the MW distribution of polymers (mainly synthetic and non-water-soluble). You can also have aqueous GPC, for water-soluble polymers, e.g. PEG; and when it is done by polymer chemists, it is called aqueous GPC, not GFC. The difference, I think, is not really in the solvent/mobile phase, but in the context, the analytical focus, and the specific expertise. The sort of polymers that chemists typically study have varying molecular weights and MW distributions, and GPC is ideal for studying these. A specific protein, say, has a definite MW, so there is no question of determining its distribution; the biochemist may be interested in analysing a complex mixture, identifying specific molecules, and perhaps separating them on a preparative scale. Along with this goes expertise specific to each context, e.g. choice of solvent, column material, and sample preparation (e.g. for proteins, denaturing or non-denaturing conditions).
Thus, although the physical basis of the techniques is the same, the distinction of name is useful because expertise in one doesn't mean you're an expert in the other. I have done a fair bit of GPC in my time, but that doesn't mean I could walk into a biochem lab and start doing GFC on proteins without learning the trade.