Is hearing loss with age supposed to be different than vision impairment?

May be. Not all elderly either become visually impaired and hearing impaired. It is hard to say which one occurs first. Visual impairment may be more prevalent than hearing loss, i presume.
Of course. In both cases, aspects of the function are diminished, however a significant portion of hearing loss is due to exposure to loud and sustained noise while younger, whereas vision impairment is either correctable like cataracts, or gradual as exposure alone does not diminish vision. This is distinct from macular changes of the very old which is a degeneration.