Yes, curl can resume partial downloads. You need to pass `-C -` to do so, which is a pretty good example of "the command line flags aren't easy to remember"
It's also yet another example of "could you please just do the right thing by default".
curl wants to be a swiss army knife, and so you'll need to configure everything just right so you don't accidentally get the bottle opener instead of the downloader. wget just downloads, and does it well.
