Rings can be connected by riveting or with butted ends. Furthermore a mail weave can consist to one half of punched rings and ring ends can also be welded together. This is usualy done for the rings of modern safety gloves worn by butchers. Besides this there are some more exotic methods like forging the ring ends into interlinking hooks. Riveted rings can either be hammered completely. I call them flat rings. For round rings only the overlapping area gets flattened and the other part of the ring retains the shape of the wire.
There are also different types of rivets: round rivets and wedge rivets. The round rivet usually has a cylindrical shape with an optional hemispheric rivet head on top. You can insert this kind of rivet from each side. The hole for the rivet can be punched out of the overlapping area or drilled instead if you don’t mind about the thin drills tending to break easily. However the hole for a wedge rivet has to be pierced with an awl for the rivet has the shape of a wedge or a cone. It can only be inserted from one side of the ring.
As you see in the side view, the inserted wedge rivet has only one protruding rivet head, which consists of material from both the rivet and the ring. You can use this in a ring weave by aligning all the rivet heads in one direction. Thus they can’t grind garments worn under the mail.