"Barbecue" is the traditional and correct spelling, whereas "barbeque" is just a confusion created by the "BBQ" abbreviation. So whenever you are in the situation to choose between these two forms again, just go for "barbecue".

Do Americans say barbecue or barbeque?

Bottom line: The standard spelling is barbecue, but barbeque is a recognized North American variant.

Why is barbecue spelled two ways?

Correction: The word barbacoa actually originated from the Taíno Indians, and refers to the wooden cooking structure they used to roast meats. It was later incorporated into the Spanish vocabulary via conquistadors who brought the cooking method back with them to Spain.