Or it's something slightly different?
"Otsumami" is the food which you eat when you enjoy drinking alcohols, like green soy beans which is a typical "Otsumami" dish and is often said to be good with beer.
"Otoshi" is the food that you are served when you eat in some restaurants where they serve alcohols along with foods at night. It is supposed to be served first, mostly soon after you take your seat and order. You can't order nor cancel "Otoshi". You don't always have to eat it, but you have to pay for it, because it is a sort of table charges for the restaurants.
And "Otoshi" can be "Otsumami" when you enjoy eating it with alcohols.