Normally, when taking a film picture, silver crystallizes at the areas exposed to light, and these crystals form the dark parts of a negative. Then a picture of the negative is taken, flipping the dark and light parts around and giving you a recognizable image.
On a tintype, the initial reaction happens on a blackened metal sheet, so the areas without silver crystals look black. Extra chemical processing brightens the silver crystals, thus directly forming a black-and-grey image without any need for a negative.
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