When people talk about 'the stock market' or 'the stock price' they are using a very coarse abstraction.
In reality for most trade-able instruments there are a variety of exchanges all operating at once. Further in each exchange there isn't a single price. There is a collection of buy and sell orders that combined together form the 'book'. For instance if you had 10 buy orders at $1 and 2000 sell orders at $1.10 what is the 'price' of that thing? The structure of the book and how all the exchanges relate (and Reg NMS in the US equities space) are all the 'market structure'.
In reality for most trade-able instruments there are a variety of exchanges all operating at once. Further in each exchange there isn't a single price. There is a collection of buy and sell orders that combined together form the 'book'. For instance if you had 10 buy orders at $1 and 2000 sell orders at $1.10 what is the 'price' of that thing? The structure of the book and how all the exchanges relate (and Reg NMS in the US equities space) are all the 'market structure'.