The ambiguity, cleared up first
"8-bit image" means two incompatible things depending on who is speaking, and this causes more confusion than the concept itself.
8 bits per channel means each of red, green and blue gets 256 levels, giving 16.7 million possible colours. This is the standard for photographs, JPEG and ordinary PNG. Photoshop calls it "8 Bits/Channel"; some people call the same file 24-bit, counting all three channels together.
8-bit indexed means the whole image is limited to 256 colours in total, chosen from a palette. This is PNG-8 and GIF, and it is dramatically more restrictive.
So a "24-bit PNG" and an "8-bit PNG" differ by a factor of 65,000 in available colours. When a tool offers to convert your image to 8-bit, find out which one it means.