not much really, both are black and white images, the only difference is intention. spec controls how light shines on a material, and it'll look pretty similar to a bump higher parts get higher values... higher values in bump will also probably have higher values in spec, but not necessarily the same values.
fine detail bumps probably wont have want much contrast between highest and lowest values, while spec usually needs a bigger difference between them.
also, when using a spec map, drop the value to 0 on the material to let it equal the image values, else it'll come out alot brighter than intended
image attached