> The "classic" american barbecue features harburgers and hotdog sausages in bread

This is definitely not classic American barbecue. This is associated with going to “a barbeque”, which is slang for a summer picnic type gathering with food (sometimes pot luck style), hot dogs and hamburgers being cheap and easy food fair. American barbecue, the food, is defined by regions, with different parts of the country being known for the animal used (beef, pork, chicken), the preparation and cooking method (dry or wet rubbed, smoked with various wood types, grilled), and serving (sans sauce or with mustard, vinegar, mayonnaise, or tomato based bbq sauce). I personally am partial to Texas beef brisket and Memphis dry rub ribs.

If someone was taking me to a backyard neighborhood barbeque, I would expect hamburgers, hot dogs, potato salad, and some weird jello based side dish someone’s aunt made. If someone was taking me to an “authentic barbeque joint”, I would be insulted if they were primarily serving hamburgers and hotdogs.

Is there an actual distinction between "barbecue" and "barbeque"? I know there's definitely a scale of quality/practicality, ranging from stuff like burgers to beer chicken to boned cuts (t-bones, ribs) to brisket/pulled pork/friends, but I thought it was all part of the same umbrella.

As a comparison, in Brazil, the homely variety of barbecue will usually not feature things like cupim (beef hump), which it's a staple of barbecue restaurants. They're all considered barbecue regardless, though.

To go back to the idea of authenticity and grammar, I don't believe chicken hearts are part of american barbecue fare anywhere in the US, picnic-style or not, whereas in Brazil they are (though typically only in restaurants). Similarly, you'd pretty much never see hotdogs being associated w/ barbecue in Brazil, and they'd have vinaigrette and potato chip strips in them.

> Is there an actual distinction between "barbecue" and "barbeque"?

No. that was just me accidentally using them both as I typed.

> I thought it was all part of the same umbrella

I think the issue comes from the food barbecue became associated with the popular family and friends get together to eat that barbecue, and once it did, was and is used for gatherings that do not contain any “barbecued” food at all. Depending on where you are in the states, “a barbecue” could be used interchangeably with picnic or pot luck.

Now, it absolutely can be argued that hot dogs and burgers are barbecue, since they are meat that is cooked by grilling. But much like the Spanish barbacoa, from which the name derives, American barbecue is usually slow cooked (typically by smoking) meat. I guess that would be the core of what barbecue is. But then you have grilled meats like burgers, sides like baked beans and potato salad that would be eaten alongside barbecue, at a barbecue. So, I guess it depends on the umbrella. If Brazilian barbecue is “a large variety of cuts of meats” I would say American barbecue is “various smoked meats, usually cooked or served with barbecue sauce” but when I think of Brazilian barbecue, I think of “chunks of meat skewered and roasted”.