Not even sure if designation is the correct term. I have no military experience, and little education. I'm researching the mater myself, but figured I would throw my inquiry out there. I don't understand how an M1 Garand, and an M1 Carbine would have the same M1 name. Then there's the M1a, M14, and Mini 14. I believe the Mini 14 is not a military weapon. I hear a lot of people use the names loosely, and sometimes refer to what I thought was strictly a full auto weapon, when they're really talking about a semi-auto weapon.

Is there any kind of organization to this? Please enlighten me to any of your knowledge.

The M1 is the Garand.
M14 is the full auto .308, 20 round magazine rifle that replaced the M1.
M1A is the semi auto version of the M14.
M1 Carbine is the 30 Carbine-chambered carbine.
Mini 14 is Ruger's rifle based on the same action design.

M1 Garand Semi-Auto US Military rifle of WWII and Korea
M1 Carbine Semi-Auto 30 cal US Military rifle used in WWII and Korea and some in Vietnam I think
M2 Carbine Select fire version of the M1 Carbine
M14 Military replacement for the M1 Garand, select fire used in Vietnam and some since.
M1A Civilian version of the M14 semi-auto only
Mini 14 scaled down version of the M1A sized for 223 size rounds. Manufactured by Ruger Semi-auto only.

Much thanks. I had all this in my head, but couldn't get it in order. Got a lot to learn. Thanks for your help.