There is only one PNG format, but it supports 5 color types.
PNG-8 refers to palette variant, which supports only 256 colors, but is usually smaller in size. PNG-8 can be a GIF substitute.
PNG-24 refers to true color variant, which supports more colors, but might be bigger. PNG-24 can be used instead of JPEG, if lossless image format is needed.
Any modern web browser will support both variants.