Wood chisels can be separated into two groups by looking how their blade is affixed to their handle. They will either have a tang or a socket.
Chisels with tangs have a piece of metal (usually a spike) forged onto the end of the blade and inserted into the handle to create a strong connection.
The tang is formed as an extension of the blade and slots into a matching cavity in the handle.
Tangs are found on chisels designed to be manipulated by hand only (not struck with a mallet). If you strike a tang chisel with a mallet you risk shattering or splitting the handle. Most chisels with tangs have a ferrule (metal ring) around the the front end of the handle which reduces the chance of the handle splitting.
Chisels with sockets are where the neck (or shaft) of the chisel is hollow (typically conical) to receive a mating handle.
The handle is shaped to fit snugly into the hollow socket part of the chisel’s blade. The friction created when the wooden handle is inserted keeps the fit tight and secure.
Socket chisels are more often used in conjunction with a mallet. The repeated blows from a mallet actually help to strengthen the frictional bond between handle and blade.