While i won't aim to provide a full and perfect definition: a phone is a computing device with a generic interface and the goal of being a platform for a wide variety of software aimed at many different goals: 1-on-1 communication (calling), messaging, social networks, document exchange, note taking, web browsing, photography & photo editing, video & video editing, inventory, physical access control, ... Consoles have a game-targeted interface and a singular focus on games.

I don't know if everything that has been labeled a console matches this description. Some "consoles" have indeed been stretching any meaningful distinction to or even past the breaking point.

But I will unashamedly go "no true Scotsman" on those: If a machine has a secondary (tertiary, quadrutionary, ...) specific focus with dedicated interface, it might still be a console. Illustration: a console that also can play dvd's ia a dedicated dvd interface. However, if the interface is generic and just waiting for the right app, not so much.

The point is not "can it do general-purpose computing" - a lot of devices can be made to run some linux. The pertinent question: is it made to support general-purpose computing out of the box? Things that I would call game consoles aren't - they're platforms for gaming.