The ship had triple shielding in the book, but our "anti-Mary-Sue" heroine couldn't figure out how to operate this technology; what we saw happen was that the ship had one set of shields up, the enemy burned through them, and then the heroine struggled to get another set up (and failed). Perhaps "triple shielding" was always meant to be a succession of shields, with #2 applied when #1 fails? Or perhaps our Lieutenant Piper just didn't have clue, and a proper mode of operations would have #2 applied on top of #1, and #3 on top of #2, all the time?
But yeah, the ship had physical armor, too. Not amounting to much when the shields were down, it seems.
Personally, I'd prefer the idea that most starships after the ENT era have two distinct shielding systems or modes: bubbles and skintights. These can be referred to collectively, or then described separately - but very few people would bother to describe them separately because they aren't usually operated separately. And the people who go for the separate description can't agree on the terminology, exactly because it's so rarely used. Most just say "shields" or "deflectors", which are synonyms in the "lift"/"elevator" vein, but some apply obscure or arcane terms like "screens" or "forcefields" to indicate the components of the system.
Only "navigational deflectors" or "beaming shields" are truly separate systems for separate purposes, as the name explicates...