A market order is an order type that regardless of the price will try to fill the amount (size) inputted. The average price depends on the available bid/ask that is on the orderbook. For example, if a market buy was executed for 1 Monero (XMR) and on the orderbook there was sell for 1 XMR for a price of $54.99 then that trade will successfully execute for at a cost of $54.99 (ignoring fees).
Alternatively, if there was 0.5 XMR at $54.99 and the other 0.5 XMR at $60 than the average price would be higher overall ($57.49).
A limit order is an order to buy or sell an asset at a specific price or better. A buy limit order can only be executed until the limit price or lower, and a sell limit order can only be executed at the limit price or higher. A limit order can only be filled if there is a large enough market buying.
Limit buys are typically placed to fill the orderbook. This means your limit order will sit as an active order (unfilled order) until someone takes the order.
If your limit order sits on the orderbook and is not a marketable limit order meaning it did not execute instantly then a maker fee will be applied. Maker fee rates are generally lower fees and in special cases, a rebate will apply as is the case for level 10 accounts.