WebP is the same, it's got a lossy mode (VP8) and a lossless mode (Which is more limited than PNG, but beats it where it overlaps). But to make it more complicated the lossless mode also has lossy processing modes, where it alters the image first to achieve smaller output sizes.

And PNG is no different.

People have a long habit of turning JPEG files into PNG files, the file extension won't help you there. They also could have reduced the colour depth or resized it, all lossy operations. All it really tells you is that it can have an alpha channel.

As for AVIF, personally I don't like the format, it feels like an "open media" (But still patented) version of HEIF to oppose Apple. Like WebP it makes the (baseless IMO) assumption that a format designed to encode motion data is better at encoding still data than a format designed to encode still data. It's got all the limitations of a video format (It's got a max resolution, only supports 12bit images, and no progressive decoding), and they left out all the enhancements from WebP (The dedicated lossless mode, "lossless AVIF" files are huge and the last I checked badly supported, so nobody actually used them, and they just called very high quality settings "lossless")

A team inside of Google was working on WebP2 around the same time, that used AV1 but actually added the useful stuff like efficient lossless encoding, it got killed too in favour of AVIF.