For my own understanding... is there only a single chain of blocks for the entire network? Or is a block chain contained within a coin?
As far as I can tell so far, it seems like a block is a transaction history, involving one or more coins... yes?
Yes, there is 1 single chain of blocks for the entire network.
Each block contains some header info and one or more transactions.
The transactions move 'coins' from one bitcoin address to another bitcoin address
coins aren't actually 'things', just numbers.