The term "budget" is allusive, perhaps because it has been brought into play to keep from openly saying what might seem not so PC.
"Budget" in this case, though, can't be pinned down with a price point. It varies. I could be defined, if a point needs stated, as the point that the lack of quality as a price saving feature becomes apparent. You might find some dealers or some brands sell nothing but these "budget" lights. Some, you might find have a quality line, and a lower quality line that has apparent cuts in quality to offer a lower price.
There are some lower priced lights that are not budget lights. By the stated description, lights like Underwater Kinetics, Pelican, some brands of old established standards and such would not be bargain lights, even though it's selling prices may be lower than some "budget" lights. For example, a Princeton Tec Blast wouldn't be consdered "budget", since it's quality is great for what it is, yet it's much lower in price than perhaps a Ultrafire tactical type Surefire work-a-like.
So, at what price point? Again,the point that the lack of quality as a price saving feature becomes apparent.