You're a "whatever"-in-training. There are many ways to skirt around this, though; my business card just says, "Emergency Medicine".
However, it's also the "state of mind" thing; ipso facto, if the PGY-II is scrubbing on your case, and he says, "I'm one of the surgeons who will be operating", that is 100% true. In the middle of a peds residency in a high-volume program (or sometime during the track of any training program, for that matter), you will say, "We're the pediatricians that will be taking care of your child (when you develop the confidence to carry both yourself, and your junior partner, even if your junior has only been in the program 4 or 6 months)".
Different hospitals may have different policies in-house (eg, ALL housestaff, regardless of specialty, are "house officers", not "surgery residents", "IM residents", etc.), but you have to subdivide for the rest of the world.