Easy...
check valves are usually found in-line in a hose to prevent the reversal of flow, such as for keeping prime on a manual galley faucet. It has no air connection and works like one of the flaps that open and close in a manual bilge pump. An anti-siphon valve prevents water from continuing to flow in a hose without suction being applied, flooding a boat--such as in a raw water intake line for the head or engine. It could be a valve like a head's joker (a "duckbill" type), or it could be a ball valve in a seat that seals under suction. It's located at the top of a horseshoe-like loop in a "T" fitting that's open on one end to the outside air. It's normally closed when suction is applied by a pump (head, raw water engine), but will un-seal to admit air and stop flow if water tries to continue to flow past it once suction is removed from the on-board end.That's my attempt to simplify the answer. Hope it clarifies it for you.