Magnetic Clasp
Two magnets that snap together. The easiest clasp to use and the least secure.
Magnetic clasps close themselves, which makes them the obvious answer for anyone with limited hand mobility.
They shear apart sideways far more easily than they pull apart, so a sleeve or a bag strap catching the necklace will open it.
Better ones add a safety catch or a secondary clasp, which removes most of the objection.
When you are buying
Only with a safety chain, and never on a piece you would be upset to lose. Also worth avoiding near a pacemaker.
Clasp
The fastening that closes a necklace or bracelet. The most common point of failure and the most overlooked part of a purchase.
Toggle Clasp
A bar that drops through a ring and lies across it. Easy to fasten one-handed, and only as secure as the tension holding it.
Lobster Clasp
A spring-loaded hook shaped like a lobster claw. The most secure everyday clasp and the modern default.