A two-stroke engine runs on petrol, supplemented with two-stroke oil or 2T oil, for that wonderful smell and beautiful blue cloud.
How exactly these are mixed depends on the motorcycle in question. Either a certain proportion of oil is mixed directly (at the pump) with the petrol, or your favourite two-wheeler has a separate reservoir for two-stroke oil, usually in the immediate vicinity of your fuel tank. In the latter case, the 2-stroke oil is automatically mixed with the petrol in the fuel tank in the correct ratio.
All two-stroke oils in this category of products are suitable for both systems.
Just like motor oil for four-stroke engines, two-stroke oil is divided into mineral, semi-synthetic and full-synthetic varieties. You can find out which of the three is suitable for your specific motorcycle in the motorcycle owner's manual, or via the Eurol product finder.