It seems simple enough. Aspirin makes you healthy, which is why it's medicine. Arsenic makes you very unhealthy, so it's poison.
But what about alcohol? Alcohol ruins our balance, our livers, our kidneys, and enough other things to be considered a poison. But it also relaxes people and makes them happier and more energetic, so it is a medicine of sorts, too.
Colloquially, alcohol is referred to as both a poison and as medicine, depending on the circumstances. It is a curious substance, being both poison and medicine, depending on what you need.