Is the shield part of your ship, or is it being emitted by it?
Both actually, the ship emits a shield, but the shield is also limited to a small area thus the emitters have to be pointed in a specific direction. And then moving the shield would require the emitters to move as well, and if you don't move the emitters yourself they are locked in place thus dragging the rest of the ship with them.
Shields being adhesive is another thing entirely. As far as I understand "shields" in Starsector are not real shields in the traditional sense of the word. They are localized gravity phenomena that distorts incoming objects and energy, something like a line of tiny, weak black holes wither stopping, compressing or diverting the projectiles in a harmless direction.
But why wont the shields rip apart everything it touches then? Most things are to big to be affected. The shield cant direct its energy in one direction along its entire length, therefore other ships are to massive to be flung in a random direction, not to mention the shield cant apply enough acceleration along such a large area to move a ship in any significant fashion and then reacts as if they ran straight into a wall, the same thing happens with missiles and asteroids. Only reason those collisions usually don't do much damage are the lack of speed.
This also explains why different damage types do different things:
Kinetic are fast and heavy objects that need lots of energy from the emitters to shift.
Explosive is not concentrated enough to do its full damage to a shield.
Fragmentation is sort of like kinetic, but its several small low velocity rounds instead of massive high velocity ones thus need only a fraction of the energy to shift compared.
Energy is energy, projectiles act like kinetic, but don't have the concentrated mass and are therefore more effectively dissipated over a greater area of the shield, beams have no mass and therefore does nothing to the integrity of the shields resulting in to need to calibrate the emitters, but continued input of energy into a shield like that takes energy of its own to compensate.