@feruze-- Salametti is just "small salami" so the history of salami and salametti are pretty much the same.
I know that the word "salami" comes from "salare" which means "to salt". Salami and other Italian charcuterie are made by salting and drying.
I don't know when salami and salametti were introduced to other regions but I think it's probably fairly recent. The history of salametti goes back to the 16th century and mostly it was made from pork. Beef salametti itself is much more recent than pork. If pork is not eaten at all in the Middle East, they may have been introduced to it much later when beef salametti became popular.
It might have been developed simultaneously too. I think all nomadic cultures have a history of using salt to preserve foods. So I wouldn't be surprised if different versions of salami and salametti were made simultaneously in other parts of the world.