'chip' is a phrase used from the beginnings of ECU remapping where a pyhsical chip or EEPROM had to be physically re-soldered into the ECU. It is still usually an off-the-shelf 'map' put onto/into the ECU.
A 'remap' is the same as above but perceived to be better - however is still the same off-the-shelf map or settings, except applied via serial/diagnostics ports.
The only difference is how they are applied to the ECU. The only time these 2 differ is where it's a custom map vs an off-the-shelf map. A custom map should be written specially for your car, on your car, and usually done on a rolling road, with fine tuning on the open road.
In this day and age the two terms are frequently intermixed and usually mean the same thing (depending on car/era). For a road car on stock ECU I think an off-the-shelf map/chip/remap is fine. You'd rarely be bothered with paying over the odds for that last couple % of difference - except where the car is highly customized or running an aftermarket ECU.
I've got a Revo chip/remap/super-go-fast-stripes on my car, and found it great - had the SPS1 option switch to disable the 'performance' map, often thought it a waste of money, expcept when the clutch start to slip and was able to switch the car back to stock power and drive on until able to replace the clutch.
From my own experience I'd go with Revo again, or else on a new Mk4 or Mk5 would look at the extra options from Revo or APR for security or extra power, some neat little boxes of tricks available these days. But at the same time, people like Logic Automotice / Upsolute do offer really great bang-for-buck ! (Probably half of a Revo + SPS1)
Tom