Brush in overlay (multiply/whatever else) mode works directly with existing pixels, so any extra strokes will deepen its effect;
when you paint with a brush in default mode on a overlay (multiply/whatever else) layer, it does not affect pixels below and there's a certain threshold for its effect on underlying material.
I can't come up with a more clear explanation, but basically - yes, you will get different result from those two
from my experience, when you're doing rough colour blocking, it's better to use layers since they're non-destructive to your original work;
when you're adding finishing touches (like colour dodged highlights) it's better to flatten your image and paint stuff in directly.
(There's also another option, painting with various brush modes on a transparent normal layer, but it has never done anything good for me, so I don't use it at all)
on the fourth day of glitchmas my painter™ gave to me
four random crashes, three broken brushes, two system hangups & one corrupted workspace