Semi vs full-auto is a conversion that should almost not need further definition however there seems to be a huge amount of misinformation (disinformation?) floating around the subject.
The prefix semi- refers to “half” or “less than full”. So, by definition alone semi-automatic would refer to a weapon that is less than full-automatic (machine gun). Yet, many conversations and even news agencies tend to treat them the same.
Here is the simple answer. Semi-automatic refers (when talking about firearms) to a weapon that is able to self load. However it is not capable of full-automatic (machine gun) fire. When the user pulls the trigger a single round is fired. As the weapon cycles its mechanism the spent case is ejected and a new cartridge is placed into the firing position. The new cartridge WILL NOT fire until the user removes pressure from the trigger and then pulls the trigger again. At this time the entire process continues. A semi-automatic rifle CANNOT be correctly identified as a machine gun.
Full-automatic weapons usually (but not always) have a semi-auto function but also have an additional select-fire setting that allows the user to hold the trigger down. The weapon then cycles continuously until the trigger is released or the magazine runs empty.
Which is legal in the United States?
In the United States a citizen can purchase a semi-automatic rifle or pistol (there are some exceptions due to local laws) as long as their 2nd Amendment right has not been taken away (adjudicated mentally deficient, current felon status, etc). Full automatic is off limits to regular citizens except for rare instances. Full automatic firearms are registered on the NFA.