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Brushed and Brushless motors

Combat RC / ESC/BEC controllers and motors- Brushed and Brushless

Hey LMR I was hoping you could help me with a few questions the internet/google cannot fully teach me haha.

So I am thinking about maybe making a combat robot/battle bot (http://www.robotmarketplace.com/therobots.html) whatever you want to call it with some left over cash. So I have some questions on Brushless and Brushed motors.

What is the difference between Brushed and Brushless? So far I understand that one has three wires and the other two- +, - , brushless has a servo wire( to make it simple for me ;)    So what am I missing? Is one geared or what?