There are two main types of secateurs: bypass and anvil. There’s no huge difference between the two and much rests on personal taste. You can see from the pictures that bypass secateurs have a more scissor-like look whereas anvil ones resemble a parrot’s beak
Here’s a quick definition of the two:
Bypass: These pruners mimic the action of a pair of scissors. The cutting mechanism is comprised of two hardened blades that bypass each other. The main benefit is that the cut is cleaner (than anvil-style secateurs) and requires less force.
Anvil: Rather than having two scissor-like blades, anvil pruners consist of a single blade and a flat, anvil-like, surface. The result is more of a “crushing” mechanism. The comparative benefit of anvil secateurs is that they can work well when slightly blunt and are able to cut through slightly thicker branches.