TSI is an evolution of TFSI
TFSI is engine EA113, TSI is engine EA888.
"This latest EA888 family of internal combustion engines is anticipated to be an eventual complete replacement of the EA113 range. It was wholly designed and developed by AUDI AG. The only common feature with its predecessors is the sharing of the same 88 millimetres (3.46 in) cylinder spacing - which keeps the engine length relatively short, meaning it can be installed either transversely or longitudinally. Grey cast iron (GJL 250) remains the choice material for the cylinder block and crankcase, due to its inherent good acoustic dampening properties. This all-new EA888 range is notable for utilising simplex roller chains to drive the two overhead camshafts, instead of the former engines' toothed-rubber timing belt. Like the final developments of the former EA113 engine generation, all EA888s only use the Audi-created Fuel Stratified Injection (FSI) direct injection. Furthermore, EA888 engines are also able utilise the Audi-developed 'valvelift' technology, which complements the existing variable valve timing. This new family of engines is scheduled to be universally available for all markets on five continents, within all marques of the Volkswagen Group. The former EA113 range still remains in production." -Wikipedia
EA113 has its dip stick in the middle in front of the cylinder block, EA888 dip stick is on the left hand side on the driver side of the engine bay. EA888 runs happily on 95 octane, will run on 91 octane. EA888 tends to start producing maximum torque anywhere from 100 rpm lower and max power 500 rpm lower. Slightly lower revs required to produce torque and power make it easier to get better fuel consumption.
EA888 more complex Engine Management unit makes it harder to put on a different mapping but result can be better because of more interpolated mapping points and better fuel system mentioned above.
Also EA888 (TSI engine) comes standard with a stronger block and Audi's equivalent of the HPF pump upgrade for 2.0t FSI engines.