Hmm not quite right but close.
VAG joined the direct injection petrol engine movement with the FSi engine. This stood for Fuel Stratisifed Injection. Basically the engine had two modes of running. Homogenous where the engine ran pretty much as any other petrol engine (except the fuel is injected into the cylinder rather than the manifold), but at certian conditions it changed into stratisfied mode, this was the ultra lean uber economy mode, flaps altered in the inlet manifold changing the air path and making the engine run lean effectively. However it was pretty much a dismal failure. It required 100+ RON fuel to work so never did and then jammed up causing problems. So the next generation came about. FSI was dropped, TSI came about.
All the charged FSi engines are now called TSi (regardless of if it has a super charger and/or turbo)
The 1.4 TSi is a 1.4 turbo, and the 1.2 TSi is a variation of that. The 1.4 Twincharger started it all off in the Golf GT and is now fitted in our cars.