Strength has a lot to do with your neurological efficiency. People who train properly for strength are able to recruit more muscle fibers to do the job more efficiently.
Let's say you have larger arms than another guy.
You can curl 100lbs for 1 rep and use approximately 70% of your muscle fibers to complete the lift.
The other guy with smaller arms can curl 115lbs for 1 rep and uses 85% of his muscle fibers to complete the lift.
The other guy has is stronger because his nervous system works more efficiently and recruits more fibers to do the job.
Now I'm kind of getting ahead of myself, but muscle fibers only increase in diameter. They do not increase in number(Increase in total number of muscle fibers has been shown in animals but is not likely to happen in humans). So even if two guys have the same size muscles, one guy can be significantly stronger than the other.
Well, I started to get away from the subject but i got to go!
Hope that makes sense.