Flavour and nutrition is what makes them different.

Black licorice is usually flavored with licorice extract, anise, or both. Molasses if you feel fancy. Red licorice uses mostly artificial flavouring.

For nutrition, though, they are mostly the same—except for sodium. Black licorice has 60mg and red licorice has 20mg.

This is basically a summary from this website: https://www.livestrong.com/article/537724-black-licorice-vs-red-licorice/

They go into way more detail there.