Maybe 'chili sauce'? This recipe has no tomatoes, just peppers, but it's a sweet-and-hot sauce:

Here is a link that might be useful: Bernardin Singapore Chili Sauce

Sounds like you are looking for what's called a flavored vinegar. Flavored vinegars are made by brining the hot peppers in vinegar in the fridge and over time the vinegar takes on the flavor of the peppers or whatever. It can then be used as a vinegar with pepper flavor or be pureed into a sauce-like consistency.

Things like tabasco are fermented sauces made with pepper mash and salt and fermented for months first, then add the vinegar and puree.

Dave

Here is a link that might be useful: NCHFP - Flavored Vinegars

That's what I am looking for to, like Tabasco or La. hot sauce.

Tabasco and La hot sauce are fermented hot sauces. Totally different
method of making than flavored vinegar. Lots of discussions on making
fermented hot sauces over on the Hot Peppers forum but fermented sauces
are generally not for canning, just for freezing or fridge storage.
Dave