Before discovering the EU, I always thought that the Stormtroopers were all clones. Now I know that they're actually all regular human recruits, at least in the current canon, but then why did Lucas in the PT decide to make Clone Troopers almost identical to the Stormtroopers? I've been thinking about this for years, but I've never found a satisfactory answer. Is it because they are the same thing for Lucas? What's the "Lucas canon" answer for this?
Clone troopers were originally a clone army created on Kamino. They formed the basis of the Grand Army of the Republic during the Clone Wars, created after Chancellor Palpatine was granted emergency powers to create an army for the Republic in order to combat the growing threat of a Separatist army of battle droids.
The Republic eventually became the Empire and started replacing clones with recruits. After the fall of the Empire, the First Order launched Project Resurrection to train children from birth to be soldiers, filling out their ranks with a new generation of stormtroopers - this is how Finn came to be a stormtrooper.
So, Clone Troopers and Stormtroopers are so similar because one is a direct descendant of the other.