Part of the problem in dealing with issues such as this is that terms get tossed about that are either political, but not technical, or based on the reporters' firearms knowledge that mostly comes from Hollywood movies.
So, "machine guns" have been illegal to own since the 1980's. Those work by offering continuous fire as long as the trigger is engaged. There have only been three crimes committed with legal "machine guns" since 1934.
An "automatic weapon" is a machine gun, so ditto above.
"Assault rifle" or "assault weapon" doesn't have a fixed legal definition. It seems to mean "rifle that looks scary".
A "semi-automatic" weapon is one that re-loads every time the trigger is pulled. This action is common to handguns and also many rifles used for hunting or predator control.
A Glock is a semi-automatic handgun.
An AR-15 is a semi-automatic rifle.
[If you're wondering how a surfer who funds his adventures by working as a parish priest knows such things, my secondary MOS was 2111. That, and I'm a hillbilly from Ohio.]
Before anyone hyperventilates about "machine guns", etc., having viewed the scene via the British newspapers [who offer many more photos and graphics], and seizing what I recall from ancient training, the concert field was a perfect target. With a common bolt-action rifle [one that needs to be re-loaded after every shot], the same terrible results could have been achieved. It was a field packed with a great number of people with limited means of egress. I shudder just thinking about it.
[Ancient training kicks in even when I don't realize it. My wife kids me when I automatically take the "gunfighter chair" in restaurants or at meetings. For those unfamiliar with the expression, that's a seat that faces to entire room and is backed by a wall. It offers a full field of vision with a protected backside, or "six".]
Update: I have since learned of an aftermarket attachment for AR type rifles that enables automatic firing. After watching the manufacturer's video, it seems likely that was what was used.