My understanding is this:
Immune to force fields means that the ship ignores the force field, acting like it doesn't exist. It should be able to both fire through and move through enemy force fields.
Fires through shields means that a ship ignores other ships' shields. Shields are not the same as force fields; ships have shields of some strength which can deflect incoming shots, while a force field is generated by force field generators, force field bearers, and exo-force fields. There was some ambiguity in the naming before, but it's been made much more consistent recently with shields being these shot-deflecting shields that all ships have and force fields being the fields that can protect nearby ships.