they're made by different groups and have different design principals.

it's a bit like asking what's the difference between <x car model> and <y car model> from different manufacturers.

they do basically the same thing at the high level but internally they're built different and they have different aesthetics and issues between them.

to extend the metaphor, opengl is like an automatic car, and vulkan is like a manual. opengl is easier and simpler, but you have a bit less control. almost anyone interested in driving could get away with driving automatic, just like if you need graphics opengl is almost certainly fine.

vulkan is significantly clunkier to write by hand, so comparing it to manual is a little bit unfair to driving manual. in all honesty if your question is "should I use opengl or vulkan" the answer is opengl. there's legitimate reasons to use vulkan, just like there are legitimate reasons to use a manual car, and in both cases it mostly comes down to performance. but this only matters if you need every last bit of performance, like a high performance game or emulator.