Chipping vs remapping?

Generally they are used interchangeably, most systems are now remapable so a company just flashes a new code onto the existing ECU EEPROM chip it used to be that ECUs had ROM chips or (WORM) PROM chips thus the actual chip was replaced. You can also get piggy back chips that sit between the ECU and the rest of the loom and alter some of the parameters going into and out of the stock ECU, these tend to be not quite as good as they normally have fewer bins resulting in a "courser" map.

Interchangeable to a point but chipping (replacing the PROM) is used when the manufacturers ECU can't be remapped.

remapping is kinda like updating your bios on a comp as i understand it where chipping is more like replacing the bios chip itself in a comp. as an example my BM 328 ECU can be remapped but my old MR2 Turbo's ECU couldn't and would need a replacement like a apexi power fc or motec ect