I'll have a go. Someone will correct my memory gaps!
Class One ... what most GA pilots had.
Class Two ... a copilot Instrument Rating. If you flew as a copilot for a non airline operator. As an example, maybe a DC3 copilot for Bush Pilots, before they got an Airline License.
Class Three ... Generally the same as a Class One, except you weren't as good! By that, I mean the tolerances for the flight test were a little looser! You couldn't fly IFR into a capital city primary airport with a Class three.!
Class Four .... Night VMC Rating
Class Five ... Ag Rating for spraying at night!
First Class ... Went with an ATPL, which you could only hold if you were a Captain with an Airline (then only TAA, Ansett,and East West)
Second Class ... For Airline copilots
E O & E