> "Assault Rifle" is a defined term as well which is basically the same as "machine gun".
The usual definition is quite distinct from the usual definition of machine gun.
> Both require the weapon to be "select fire" which means it can be set to fire more than one round per trigger pull.
Actually, no; the term is "selective fire", and while that's part of the usual definition of an assault rifle (which typically have semiautomatic, burst, and sometimes full-auto modes), it's not for machine gun, and machine guns are quite often full-auto only. An assault rifle also is a weapons that is deisgned to be fired unsupported (though it may also integrate a bipod) and which has a fixed, folding, or telescoping butt stock. While a machine gun may have none of those things, and may be designed to be fired only mounted.
> In actuality, an AR-15 is the same as any other semi-automatic rifle in function.
AR-15 is problematic to categorize, since the original Armalite AR-15 is a selective-fire traditional assault rifle, and other rifles to which that moniker is applied (which is sometimes used as a catch-all for the whole family of variants of that original design, which the US military adopted as the M16 series, and the M4 series) may either also be selective-fire assault rifles or civilian variants of the same design with variations in a few key components that render them semi-auto only.
At the same time, Colt currently markets a subset of it's line of civilian semi-automatic variations of that design as the AR-15 line (which was done after the Federal Assault Weapons ban specifically to take advantage of the AR-15 moniker's association with assault weapons.)
> For example, many states list the AR-15 as an "assault weapon" (made up term with no concrete definition)
Every state that has an "assault weapons" law also gives it concrete definitions. Typically, that's done by identifying both feature sets and a set of named existing weapons which are included (along with any copies or duplicates) regardless of whether they meet the feature sets.