Basically the different types of tournaments break up the chaos of so many older "power" cards affecting the current environments... which would be type 2 and extended... type 1 and 1.5 are the "oldest" formats as they include all cards - except ante and a few banned cards...
Type 2 is a "block of cards that must be from the following sets(some of these may be in earlier sets but have been reprinted)...
7th edition, Odyssey, Torment, Judgement, and Onslaught
Extended adds sets back through Tempest Block...
Any cards before those sets and not reprinted are part of the 1 and 1.5 formats...
A good place to look up cards and sets is
here ...
Most tournaments nowadays are TypeII as most new and old players will have cards from these sets and be able to play in the tournaments with "legal" cards...