The main difference between anvil and bypass secateurs is the type and number of blades they have.
Bypass secateurs have two cutting blades that pass over each other, like scissors. These are ideal for cutting soft-green stems, as the cut is more gentle and less likely to damage or bruise delicate stems.
Anvil secateurs have just one cutting blade and a flat, metal cutting board. Like using a knife on a cutting board, the cutting blade is pressed down to meet the board, giving a powerful cut with little force. Anvil secateurs are ideal for cutting thicker, wooden stems or dead wood.