The term you are looking for to describe the M16 is "assault rifle". Assault rifle is the term generally used to define rifles that are capable of full auto or burst fire (not in a legal sense however).
"Assault weapon" is an actual term, but it is a rhetorical, and later legal, construction, used to describe some semi-automatic firearms. Not all semi-automatic firearms, just some of them.
Looking over wikipedia,
the "history" section for the assault weapon article is fairly accurate so if you want to look into the origin of the term, that's not a bad place to start. Short story: the term was either created as slang by gun importers and enthusiasts to describe the influx of military style semi-auto weapons (mostly rifles) that started appearing all over in the 80s and later appropriated by gun control groups because it's a great term if you don't like those kinds of guns, or it was originally created by gun control groups (because they don't like those types of guns). I remember reading about the history in more depth years ago that lead me to subscribe to the former theory, but I can't find the posts that dealt with that subject at the moment to provide more detail so I will leave it at that.
Anyway
For all practical rhetorical extents and purposes "assault weapon" is a term used to describe "semi-automatic rifles that look scary/"military style"". It's a brilliant term because you can get away with calling a gun that isn't an "assault rifle" (semi-auto rifles are not super regulated in the USA) something that sounds a lot like "assault rifle" (assault rifles being highly regulated around here, but legal to own with significant paperwork and money), and thus leave people with the impression that legally owned assault rifles are on every street corner (they aren't) without technically being factually incorrect because "assault weapon" doesn't mean "assault rifle".
For legal purposes the term "assault weapon" varies in definition from state to state (in the USA). Some states do not have assault weapon laws. Others do. In the case of Orlando, the weapon used in the shooting is not legally an "assault weapon" in Florida (iirc, FL doesn't have an assault weapon ban), whereas in NY State or California, it probably is (as both those states have assault weapon bans). As a broad generalization, the definition of assault weapon will typically fall into two categories:
One category is make/model prohibitions, usually meaning there's a list, and if the gun's name is on that list, you can't have it. Lists such as these usually become outdated as manufacturers change names and models to get around this. For example, the AR-15 is banned in California. But that's just the Armalite model, so you can walk into pretty much any gun store in CA and buy something that looks like, and functions like, and is dimensionally identical to an AR-15, but isn't, because Armalite doesn't make it.
The other category is "evil feature" prohibitions. These are laws that define what "features" semi-automatic cannot have, and these features are nearly always cosmetic. Frequent offenders on the list of "features" are pistol grips, "flash hiders", folding or collapsing stocks, and vertical forward grips. It's no coincidence that these cosmetic features also make weapons that possess them look more like military arms, and in most cases the semi-automatic versions of military rifles are just manufactured with those features to begin with. Typically the way people get around these prohibitions is removing the "evil features" out of state, making the gun legal for sale and ownership in state.
Sometimes the "evil feature" definition also includes differences in the location of mechanical features. For example, in California one of the features semi-auto pistols cannot have without being classified as an assault weapon is being fed from a detachable magazine outside the pistol grip, note that pistols fed from a magazine within the pistol grip are acceptable (it's still semi-auto, and it's still fed from a mag).
Also in some cases assault weapon definitions include prohibitions against specific mechanical features, for example, again in California, any shotgun (not just semi-automatic) that is fed from a "revolving cylinder" is an assault weapon, but this is not super common (note, very few shotguns are fed from a revolving cylinder, look up the
striker/protecta to read about the fun mechanical issues that oddity had).
If you want to see what some laws look like state to state,
wikipedia is actually a fairly good place to start.