This and similar threads I've seen on other boards might be better in Trek Tech, which is a fascinating board in its own right. I strongly recommend it, but be ready for serious discussions of real and theoretical physics. It makes my head spin.
Anyway, TMOS and one of the TNG DVD extras make clear that deflectors are different from shields. The former sweeps way, way ahead of a ship, to (appropriately) deflect even dust that could pierce the hull at hyper-light speeds. I agree that they are likely something like tractor beams, but in reverse.
We can assume that deflectors are fairly weak. But they're critical -- they're in action anytime a ship goes to warp (and perhaps even at high rates of impulse).
By contrast, shields are raised only periodically, and we've seen that they're real energy hogs. (Besides canon, why not otherwise run around with shields engaged all the time?)
To make matters more complicated, we've seen and heard on-screen that shields are both a sort of skinfield, right next to the hull, and also a sort of shell surrounding a ship at some distance. TOS, which I know best, made it even more complex, by having different, numbered shield zones, which could be moved to cover each other.
As for what shields and deflectors are and what they can do, thanks to TNG we know that Geordi can reconfigure them to ward off pretty much anything but a frown or rainy day. I doubt if we'll ever be able to come up with a Treknical explanation.