A "chip" is a piggy back, some of them I've heard can plug into the ECU but for the most part a chip refers to a 3rd party programmable control unit that sits between the ECU and engine sensors.
How it works is, a circuit board with a micro-processor is inserted between the ECU and sensor, it then changes the voltages/resistance/etc. received by the ECU, this in turn causes the ECU to do what it is they wish to accomplish with the piggy back, namely increase/decrease fueling/ignition timing/etc.
So the idea is you put in the piggy back system, add performance mods, put the car on a dyno and see where the car is over/under fueling and change values on the piggy back which in turn changes the way the ECU interprets the data, causing a change such as increased fueling or decreased timing, whatever may be the case.
You don't HAVE to do any type of tuning with a chip, you can put it in and put all the values in as 0, that will cause NO change to the input the ECU receives, therefore it's back to stock, so to speak, the chip would be invisible, even to the ECU or any type of diagnostic tool, they'd have to look at the ECU wiring to determine it's there.
You only HAVE to remap if the car is having trouble running, usually this is the case if you fit a seriously wide degree camshaft in combination with other modifications such as port & flow, exhaust manifold, intake manifold, etc. On Opel's for example some people even use 1.4 Corsa ECU's on 2litre engines or fit ITB's (individual throttle bodies) and chip, these cars could probably start without the chip but it's gonna run like crap.
So you can see you only NEED to remap if you A) wish to increase performance or B) the car isn't running as it should (which includes, engine knocking, over/under fueling, terrible fuel economy, etc.)
Most of the newer piggy back system are basically a ECU, they even allow extra injectors and things to be added.
The other side of this as you may know is full management which replaces the ECU with a after market variant, might sound awesome but in reality most cars have pretty awesome stock ECU's and many of these management system lack key features like idle control, I've used Dicktator and Mr. Turbo before and I'd take standard ECU with a piggy back ANY day over those systems, they just cause headaches.
Just so you know: Most N/A cars would get NO benefit from fitting a chip or full management (in fact it'd probably be worse) if extensive mods have not been done to the engine (For example, ANY Opel N/A motor will yield NO gain by fitting a chip without mods). Turbo motors on the other hand is different, most of these yuppies who talk about how awesome their GTi is after a chip assume that the map of the standard ECU is inferior when in reality the extra power was gained by the piggy back increasing the Boost on the Turbo Charger, meaning more power but less reliable motor (and considering VW's track record so far with Turbo chargers I'd say these units are already running on the edge, increasing the boost is just asking for it to blow).
The OEM ECU is tuned by the manufacturer using engine dyno's where the actual engine is fitted to a system and carefully monitored, mobile dyno's or wheel type dyno's can't compete with that.