Taker:
When you place an order that trades immediately, by filling partially or fully, before going on the order book, those trades will be "taker" trades.

Trades from Market orders are always Takers, as Market orders can never go on the order book. These trades are "taking" volume off of the order book, and therefore called the "taker."

Maker:
When you place a limit order that goes on the order book partially or fully, any subsequent trades coming from that order will be as a “maker.”

These orders add liquidity to the order book, helping to "make the market," and are therefore termed the "maker" for any subsequent trades.

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