Suffocate. To smother is the act of covering something or someone with something else. E.g. "He smothered the biscuits in chocolate" or "She smothered his mouth with a pillow to silence his screams". To suffocate is the act of not being able to breath. e.g. "She couldn't swim, so began to suffocate underwater" or "The air was so thin that he felt like he was suffocating". It can also be used to describe the act of stopping someone else from breathing: "She squeezed his neck, suffocating him". So when we talk about someone dying, we could use both: "The boy smothered his grandfather's face with a pillow until he suffocated."

Usually you would say they suffocated. Smother is a verb used to suggest you are depriving the other person of breath. So, you might say X smothered Y. Y suffocated and died.