An 8-bit image will use 1 byte per pixel, while a 32-bit image will use 4 bytes per pixel. The color bit depth refers to the number of bits used to indicate the color of a single pixel. More bits means more colors can be represented.
This wikipedia article may provide more information and a visual comparison of the difference. http://en.wikipedia.org/wiki/Color_depth
A PNG image may also indicate a color palette, which may also be associated with 8 bits / 32 bits. In this case, if it concerned the palette, there might not have been a visual difference between the first image and the second. Again, wikipedia has more information: http://en.wikipedia.org/wiki/Portable_Network_Graphics#Color_depth
There is probably a slight visual difference between the images if they do not use an indexed color palette. However, as stated in pst in the comments below, it is possible that they both look the same.
source share