Market Maker
Market makers place orders on to the orderbook and wait till their orders get filled. Usually, a market maker will try and sell for a higher price or/and buy for a lower price. Market makers use the limit order type so that their orders don't get filled immediately.
If a limit order fills immediately it will register as a market taker order (marketable limit order). For a market maker to successfully fill an order they must wait for a Market taker order to match.
It is also important to note that market makers pay a lower fee, as they are contributing to adding liquidity to the market.
Market Taker
Market takers are participants of the market who are agreeing with the currently posted prices on the orderbook and wish to have their orders filled immediately. If the highest or lowest price is okay then submitting a market order with the amount wanted will settle the trade instantly if there is enough liquidity, this trade will register under the market taker trade since it was filled immediately and taken from the orderbook.
It is also important to note that market takers pay a higher fee as they are not contributing to liquidity and are taking liquidity from the market.