Please anyone correct me if I am mistaken on certain terminology.
Well, you asked for it
Butted maille did exist historically. There are ancient examples but in order to be effective in combat butted rings must be made from very heavy gauge wire.
Terminology as used by the retailers -
Maille is broken up by ring type, rivet type, and sometimes patterning
Ring Type -
Round - Round rings are standard rings made from bent wire.
Flat - Flat rings are more like a washer. In period round rings were whacked with a hammer to flatten them out. It increases their strength by making them much more resistant to bursting open. Modern flat rings are manufactured differently for practical reasons and are similar but not quite like real flattened medieval rings.
Rivet Type
Dome or Pin - Round headed rivets with a pin shank that secures the ends of the rings together
Wedge - tiny little triangles of steel or iron compressed in to the drifted hole where the edges of the ring overlap. The advantage to modernly manufactured wedge rivets are that they are much nicer to underlying clothing layers and it doesn't get caught on itself as easily as pin riveted.
Patterns -
All riveted - every ring is riveted (period for a lot of the 14th century)
Alternating - every other row of rings is riveted, the in between rows are solid rings that require no rivet (like a solid washer or uncut ring)
Material
Mild steel - soft steel, will rust, requires maintenance and oiling
Stainless steel - obviously not period, but they do a good job of making look like normal steel - virtually maintenance free
Period and status will dictate the type of garment, be it a short sleeved, mid thigh length garment, or a long sleeved, knee-length garment etc.