What are the individual names of these nine different PVC fittings

The schedule is the wall thickness of the pipe (essentially how much pressure it can withstand). Wikipedia has a Nominal Pipe Size Table (and the article goes into the description of the size and the why behind them).

From this article http://www.ehow.com/facts_5575151_difference-between-schedule-schedule-pipe.html:

For a relatively constant pipe outside diameter, the wall thickness varies from Schedule 10 (light) to Schedule 40 (standard weight) to Schedule 80 (extra strong) to Schedule 160 (double extra strong).

Schedule 40 pipe is typically used in construction. However, if a stronger pipe is needed, then Schedule 80 can be used. An example where Schedule 80 should be considered is if the pipe is exposed during construction. The stronger pipe is more resistant to incidental bumping by workers or equipment.

In my house the line that runs out to my irrigation system and the sewer pipe are all schedule 40 (the schedule is usually printed on the pipe).

I see no reason why you should cut threads on a PVC pipe. It seems to me that this would be unnecessarily difficult and would weaken the pipe.

You should, instead, get a slip to thread adapter and glue it onto the pipe to thread it wherever you like. Any big-box hardware store or irrigation department should be able to provide this adapter.

Edit: Here is a link to such an adapter for $1.56at big orange hardware store. :

https://www.homedepot.com/p/Charlotte-Pipe-2-in-PVC-Sch-40-MPT-x-S-Male-Adapter-PVC-02109-1600HD/203825431