During World War I, shortened versions of the Hotchkiss 6-pounder QF naval cannon were mounted on the first tanks. During World War II, it was common to equip tanks with modified versions of towed artillery pieces (e.g. the Panzer IV's KwK 40 was a modified PaK 40, the Tiger II's KwK 43 was a modified PaK 43) - the towed version of these pieces would doubtlessly be considered artillery, but the tank-mounted version is not. On the other hand, self-propelled artillery existed and was always considered as artillery (e.g. the ISU-122 and ISU-152, the M109, the PzH2000), again equipped with weaponry that would be considered artillery when towed, with the only difference that, here, the weapon's status as artillery was sufficient to transfer the artillery status upon the entire vehicle, which did not happen for tanks. The only technical difference seems to be that "tanks" mount cannon, while vehicles considered "artillery" mount howitzers. Is that the entire difference? What was the reasoning behind classifying combat vehicles along that criterion?
You're forgetting an important distinction between tanks and artillery: armour. Tanks are armoured so they can go into the assault in support of the infantry or so they can fight other tanks. Self-propelled artillery has no comparable levels of protection. Similarly, an assault gun may be armoured sufficiently to support the infantry in the attack, but lack the speed, turret traverse, or specialised anti-tank ammunition that would make it a tank.