Well, the way it was supposed to work was that the shields were supposed to around the ship and the deflector was supposed to project outwards in a specific targeted direction, but the scripts fumbled that a lot.
Different use of "deflector." That's the navigational deflector beam, which emerges from the forward dish and pushes space debris out of the ship's path. It's an idea that was worked out by the show's technical advisors and mentioned in
The Making of Star Trek and the
Concordance, but was never clearly established in dialogue until TNG. In TOS, the deflector screens/shields, or just deflectors, were a more general vessel defense. As I said, they were originally called deflector screens, but started to be interchangeably called deflector shields midway through season 1. There was never any attempt to differentiate the meanings of "screen" and "shield" until
Phase II and TMP.
Granted, in the first couple of uses, it does seem like "deflectors" is being used in a manner commensurate with the tech advisors' asteroid-beam idea. In "Where No Man," Spock orders deflectors to full intensity as they approach the barrier, and reports "deflectors say there's something there, sensors say there isn't." And in "The Corbomite Maneuver," Sulu says "deflectors aren't stopping" the cube buoy as it approaches. Those both suggest that the deflectors are something acting at a distance ahead of the ship. But right after that in "Mudd's Women," Kirk and Farrell refer to the "deflector screen" as something that can be extended around the scout ship they're pursuing. By "Balance of Terror," Hansen refers to the border outpost's "deflector shield" as a defense knocked out by the Romulans; a stationary outpost would have no need for a navigational deflector beam, so clearly it's being used in the more familiar sense. In "Arena," Sulu reports that the
Enterprise's phasers had no effect against the Gorn ship's "deflector screen." And in "Tomorrow is Yesterday," Spock said the ship's "deflectors" were blocking Earth radar beams.
So it seems like they were initially guided by the tech advice about a forward deflector beam, but generalized it into some more vaguely defined "deflectors," plural, that served whatever purpose the script required, so that they rapidly evolved into a more general, omnidirectional defense system.