Agreed. From a marketing perspective, it makes sense Apple called it a phone. People already had mobile phones on them so you had nothing to lose with the switch. Had they positioned it as a PDA¹ it might’ve been seen as an extra unnecessary device for business people. They’d need to waste effort assuring people it made calls and sent SMS messages so it could be used instead of the phone. An improvement to your current device is an easier sell than a replacement.
¹ https://en.wikipedia.org/wiki/Personal_digital_assistant