This usually means manganese, which often shows up next to iron in the same water.

Manganese stays dissolved underground and turns into a black oxide once it reaches air, so it marks the fixtures rather than the glass.

Look for gray-black smears in the toilet and dishwasher, black grit in the aerator screen, and darker laundry stains than iron leaves.

Do not buy a softener on the strength of the stain. Manganese needs a number and a pH to size anything, and the two often need different treatment than iron alone.