Special Conditions overwrite each other.
If a Pokemon is poisoned by an attack, and no other modifiers are present, they take normal poison damage (10 between turns).
If a Pokemon is already poisoned normally and then gets poisoned by an attack with a poison damage modifier (like Triple Poison), the new Poison condition overwrites the old one (30 between turns).
It works in reverse, too. If a Pokemon is poisoned via Triple Poison and then gets poisoned by an attack without a poison damage modifier, this new Poison condition overwrites the condition inflicted by Triple Poison, and they would go back to taking 10 between turns instead of 30.