The Definition I’ve always been taught:
a phone with the ability to install and run applications from an application repository (often called an “app store”) without needing to “sideload” via USB
So no, your definition isn’t inclusive of Smart Phones
Pre-smart would have the applications only be those set by a provider, and no way (without manually sideload installing via USB) to install extra applications
Edit: apparently I can’t spell “applications”, put it as “aplications”
I’d say that anything else isn’t “Smart”, it’s just a phone
Well yeah, a computer isn’t a phone