Well the main difference is that when your in a dream, you dont actually feel yourself in it, you usually just go to sleep and in the morning you have memories of it.

Lucid dreams are a totally different experience.

Instead of waking up with memories of one, you can actually feel yourself in a dream, and the whole thing happens in real time.

When you havea lucid dream you will know the difference, it is amazing to put it simply. but you cant explain it properly, because its a feeling and such a feeling cant be expressed in words...

ive said this before to somewone who asked the same question; its like trying to tell a person who has been blind all their life what the sky looks like.