It's a completely different algorithm, surprisingly, based around "predictors" from nearby previously-decoded pixels. Quite like Floyd-Steinberg dithering.
This isn't how it actually works, but one way to turn a lossy decoder into a lossy one, is to send a diff of the actual pixels vs the encoded ones. Since the lossy compression will be close to correct, the diff will mostly be small values or 0's. Which is much easier to compress.
Likewise you can turn any lossless compressor into a lossy one, by modifying the pixels that are the hardest to compress. E.g. if there is a random red pixel in a group of blue pixels, you can make it blue, and save up to 3 bytes. Or you can discard color information that humans aren't very sensitive too anyway, like JPEG does. All lossless means is that the compression isn't required by the format itself.
Well of course, JPEG artifacts aren't necessarily going to be easier for png to compress. You need to make modifications designed for png's algorithm. There are some tools that do this:
