Toxic is used to refer to the degree to which biological organisms as well as non biological organisms (in a allegorical sense) can damage you.
Poison describes biological organisms only, which will harm you, and which contain a high level of toxicity.
Anything that causes you harm can be called toxic, from an insect bite to being exposed to the cold, whereas you have to ingest (through eating or breathing) a poisonous substance for it to do you harm.