True for all damage types except Thunder (but it does more damage) if I remember correctly.
Well actualy its true only for Fire and Lightning ...
Poison (unless i remember incorectly) only gives "poisoned" status, wich gives you disadvantage, but no damage ... Frost only creates difficiult terain with risk to fall prone ... Acid reduces target AC, wich isnt damage ... but in some cases can be OP as fuck.