[Baseball Rarities]

I know that there are many different designs for baseball tickets, but I am specifically looking at the 1915 World Series tickets for the games that were played in Philadelphia.

What are the different parts of this ticket called? I assume that the top piece with the actual seating information is the proper "ticket stub."

Is the middle piece referred to as a "rain check" or is it also a ticket stub?

Here are images of the separated top portion and a middle portion along along with "stub" that still has the two pieces attached.

What are the correct names for each?