This is where we get into the problem of technological evolution. Back in the day, until a simple mislabeling led to something propagating down through fandom... On the TOS Enterprise, Gene, in the writers' bible, was very clear the ship had two related but distinct defense systems: Shields and deflectors. Shields are a layer of energy around the ship, like, as you say, a nonphysical extra hull layer. Deflectors are the active beams that push small objects out of the ship's path. "Deflectors" and "deflector beams" were synonymous. There were no "deflector shields". I remember deflector screens at one point, and need to run that down.
We see in TWOK, TFF, and TUC that shields are conformal. And, further, in "Encounter At Farpoint", Worf, as Deputy Tactical Officer (under Tasha) reposts, "Shields and deflectors up, sir". On the original ship, the shield generators were built into the hull. The deflectors were emitted from the three boxlike structures flanking the main sensor dish. That carried forward to the TMP refit. The guys at ILM asked about hull structures to make sure nothing was left off, and they included the refit-style deflector emitters on the Reliant -- two built into the saucer, one on the torpedo pod. It is only lacking the big long-range sensor dish. The Excelsior, too, has deflector emitters in the neck, a main sensor dish, and its forward torpedo tubes are in the "gunwale" off to the sides, at the top of the secondary hull.
Starting with the Ambassador class, the big dish is a combined unit, carried forward with the Galaxy class. The dish now generates nested passive deflector screens that repel microparticles, as well as the active beams. The passive shields also act as a first line of defense/early-warning system for anything coming in. In "The Outrageous Okona", when Worf reports the Oronaran ship is locking lasers on them, Picard comments that lasers "won't even penetrate our navigational shields". Those are also the layer of shields being referred to when they "extend shields" to surround another object or ship. They wouldn't stand up to a real attack, but can dissuade casual hostility.
Also, in the series, they can't damage the miniature too badly because they don't have the time to make replacement panels or the like -- never mind the use of stock footage.
