I'm not an FB user, but I might as well be, since I have an Instagram account that I mindlessly scroll from time to time.
Here are some examples: https://imgur.com/a/7YVH3ch
There are likely thousands more, that's just the browsing section.
The targeting is relatively specific. Think of a (general) category and it'll be available. I use it for bars and restaurants at a local level, and the granularity is quite nice vs other media (target people who like bars or restaurants, are into music, are into drinks, are into cocktails, are into concerts currently in the city or who are traveling to this city)
It really helps a small budget go a long a way, assuming the stats they give are correct.
And herein lies the rub.
In all seriousness, I wouldn't doubt that either - spend more, target more. But based on the screenshots someone else posted up a bit, it's pretty granular (I presume) by default.