"AR" stands for "Armalite Rifle". Armalite was the company founded by innovative weapons designer Eugene Stoner who designed the M-16. As the patents have expired on most of his designs (from the 1950s and early 1960s) many different companies build AR pattern rifles and parts for AR pattern rifles.
The AR "lower reciever" is (as the brief explains) the part of the rifle that has the serial number and is considered the gun by the government for the purpose of various gun control laws. It is possible, with the right tools and plans to build a 100% compatible AR Lower Receiver from scratch.
This is what a commercially manufactured AR-15 lower reciever looks like. All other parts of the rifle are attached to it. The grip, trigger group, butt stock w/ recoil tube, and upper receiver with barrel and bolt assembly.
Apologies in advance if this is not what you were asking. Hopefully someone else reading this article might find it helpful.
The rifle was adopted by only one NATO country, Portugal, around 1960. It saw use in their colonies in Africa, Angola and Mozambique. Note the brown colored stocks and charging handle inside the carrying handle.
The US Army liked the gun and asked Stoner to scale it down for use by smaller stature Vietnamese troops. The result was the M-16, in caliber 5.56x45mm. Which is now America's longest serving main military service rifle.
Original M16A1 military style AR-15.
Another Eugene Stoner design was the AR-7 survival rifle. It was chambered in .22LR It was also quite innovative - the rifle disassembled without tools and the parts all stowed in the hollow plastic buttstock, which was claimed to float when stored this way. It was created as an emergency pilot survival weapon, where it's light weight was a virtue.
Eugene Stoner died in 1997. Here's his bio on Wikipedia: Eugene Stoner