A market order is an instruction to the trading system to execute the buy or sell transaction at the best available market price. The trading system automatically executes the order immediately at the best price available. While placing a Market Order is not an issue with highly liquid index stocks, it could be an issue with illiquid stocks. In the case of illiquid stocks, the market order could get executed way off the intended price visible on the screen. Hence it is always to check the market volume depth of bids and asks before placing a market order.
A limit order is a price limit that is set for the order. The trading system will execute the buy order at the limit price or better (lower for buy orders and higher for sell orders) and will execute the sell order at the limit price or higher. Once the order is placed as a limit order, one can go to the order book on the trading platform and check if the order has been executed or not.