Everyone's a comedian.
Um, well, there are a few things wrong here.
The AR-15 and M16 are almost the same rifle. The only difference is the selector. The M16 has Safe/Semi/Burst modes while the AR-15 only has Safe/Semi. They both have fixed stocks and 20" barrels.
The M4 comes with a 16" barrel and a collapsible stock.
Now, there is an almost infinite variety of configurations these come in. The most common in the military is still the M16 (actually the M16A1 or M16A2). In the Air Force, the M4 is the most common amongst the Security Forces. At least it's what I see every day. Select units with special missions can have rifles or carbines in almost any configuration. Rest assured, the military will have a specific designation for each one, but I don't know what they are. So, while some units might have carbines with 14.5" barrels, they are not common. Also, they would be issued to units who are specifically going to urban areas.
Is a longer barrel more effective at longer range? The common wisdom says yes, but there are some who say not. I have been researching this very subject a lot lately. Suffice it to say, at distances of 500 meters and less, the difference between 20" and 16" barrels is nil.
That's the short version. If you want the long version, including supporting facts, start a new thread.