Think differently... I'm not sure that's true, but if you're never exposed to visual stimulus there is a lack synaptic growth in the visual cortex. You still have the equipment to see, but the brain hasn't been stimulated to form networks needed to process visual input. I think the best way to think of this is not so much that there is a difference, but that the "firmware" for sight is never initialized... there is nothing to tell that part of the human computer what to create for the mind's eye.
I think you're close with the processing of information, but the thought process... who knows? There are people with sight who have dyslexia, or are synesthetes, or see number forms, or have eidetic memories... they arguably process information differently. I don't think that makes them think differently as much as the internal process is altered, with the input and output ultimately matching in the end.