A few years late, but I think it contributes. The Curve Tool can directly do anything that the Levels tool can do. And a bit more too, but the curly curved "curve" part is simply one option, but the Curve tool has several other features which directly match Levels. The Curve Tool is perhaps more graphical than Levels, but both show the histogram background.
In Levels, if you move the White Point in (say to 205), then that tone will become the brightest at the 255 end (and the original 206..255 if any will be clipped at 255). If you set the Black Point in (say to 30), then that tone will become the darkest at 0 there (and the original 0..29 if any will be clipped at 0).
In Curves, you can do that same thing, but you can always see a direct graph of the conversion of those numerical tones... of every tone.
It was prepared to answer similar questions very directly, and my site has an example of the several comparable options of Curve and Levels, and specifically how the same things (many same things) shown done by both tools, which IMO can also give a good idea of the features and working of the curve. The idea becomes easy once we realize that both tools are just manipulating the 0..255 response. The Curve response is directly "input this number, and get out that number" (speaking generally, not precisely number for number).
It's too big for here, but you are invited to view it at https://www.scantips.com/curve/