Differences between "stasis" and "stopped"?

Time Stop is an effect that makes the target Invulnerable while unable to do anything for a short duration of time. The target is locked into his position and can't be interacted with. Unlike Stasis, Cooldowns and Damage over Time effects don't refresh during Time Stop. Time Stop can affect Invulnerable and Unstoppable heroes, but not heroes in Stasis.

Stasis is an effect that makes the target immune to damage and untargetable, but also makes them unable to use their abilities and in (most cases) move for a short duration of time. Stasis also removes existing debuffs, including Armor debuffs and hero specific debuffs like Jaina's "Chill". Most abilities that grant self-Stasis can be cancelled to end the effect early. Stasis still allows Cooldowns to refresh as opposed to Time Stop. Unlike Invulnerable targets, heroes in Stasis can not be affected by friendly abilities. Zagara's Devouring Maw is the only stasis effect that allows damage to be dealt to the target and targetting Unstoppable enemies.

Think of these abilities as pauses - time stop makes you pause the game and your character is removed from the game for a bit, then comes back the exact same as when it had been removed - stasis makes you pause the game your character is NOT removed from the game but just in a timeout.