True. A "Bobber" is a bike that has been stripped of anything that doesn't contribute to the operation of the motorcycle. If it's not absolutely necessary to make it run, it's outta here.
"Choppers" evolved out of the "Bobber." When folks were building Bobbers, they added slightly extended front ends for the sole purpose of having more ground clearance; a firmer, more responsive fork; and better handling all around. Then Bobber Bob decided to extend his springer twice as long--from 3" to 6". Then Dangerous Doug countered with a 9" over...and then it just got ridiculous.
The best way to describe it is that Bobbers are more performance-oriented, whereas Choppers are more style-oriented. The line blurs as they approach a common branch on the MC Family Tree.