If a Buyer submits an order for buy price of $10 and a Seller submits an order to sell at $8 - does the price sell at the Buy or the Sell price?
That depends on the order of the orders.
If the buyer submits first, there is a buy order of $10 in the order book, and the sell order gets fulfilled immediately at $10.
If the seller submits first, there is a sell order of $8 in the order book, and the buy order gets fulfilled immediately at $8.
But maybe I should phrase it differently and in a more general way:
If an order is placed which cannot be fulfilled, it is placed into the order book. There should be no difference between different exchange systems.
If it can be fulfilled with an already existing order in the order book, the price is usually the one in the order book, but here there might be differences between exchange systems - maybe the NBBO system in the USA works slightly different.