An ArmaLite 15 (AR-15) is not an assault rifle. It's a semi-automatic (which means, one trigger pull = one bullet, and the rifle automatically loads another round for you without you having to manual use a pump, lever, or bolt mechanism to load it yourself) rifle than shoots a relatively, albeit incredible fast, small rifle round. Commonly, it can be describe as a varmint rifle.
An assault rifle is normally a rifle that has full auto capabilities (one trigger pull = more than one bullet), firing a small intermediate-sized rifle round. This would include the military version of the AR-15, the M16, as well as the AK47.
Yes, both the M16 and AR-15 look similar, which is why people like yourself can't tell the difference. But, they are not the same gun (despite what the media wants you to think). The AR-15 might look black and scary, but they do come in pink with hello kitty stickers if that's more your style.