Yes, identity theft includes things as basic as using someone else's credit card. I learned that when I reported that someone rifled through our car, took a credit card, and tried to use it at a gas station.

It kinda surprised me.

This Mitchell and Webb skit feels relevant https://youtu.be/CS9ptA3Ya9E

He stole your money and both your identity (when making the transaction, as he is not authorized). Just pondering, not a lawyer.

It is rare relative to stolen credit cards. But I wouldn't call in excess of 700,000 cases/year to be "hardly ever".

See https://bjs.ojp.gov/content/pub/pdf/vit14.pdf for comparative numbers for 2012 and 2014.

That 700k is not referring to someone actually assuming someone elses identity. A tiny fraction of them might be, but tax return fraud or unemployment fraud seem like far more likely options.