Which tool for which job
The names overlap enough to be confusing, so briefly: converting changes the format, compressing keeps the format and reduces the bytes, resizing changes the pixel dimensions, and cropping changes what is in the frame. They are often confused because all four can make a file smaller, but only one of them does it without throwing away something you might want.
When a file has to be much smaller, resize before you compress. Halving both dimensions removes three quarters of the pixels and costs nothing visually at the size the image will actually be displayed; achieving the same reduction by pushing compression harder puts visible artefacts everywhere. When both are needed, crop first, then resize, then compress — each step then works on less data than the one before.
Why the list is shorter than you might expect
Several obvious conversions are missing on purpose. PNG to SVG and JPG to SVG are absent because turning a bitmap into vector paths requires tracing, and the common shortcut — wrapping the bitmap in an <svg> tag — produces a file with the right extension that is not a vector at all. WebP to GIF is absent because writing an animated GIF needs a real encoder, and silently dropping the animation would answer the wrong question.
A page here means the tool works and the page says something specific about that conversion. That is a slower way to build a site, and it is the reason there are dozens of pages rather than hundreds.
Everything runs on your device
The codecs — mozjpeg, libwebp, libavif, oxipng, libheif, resvg, pdf.js — are compiled to WebAssembly and run in a background thread in your browser. There is no upload step because there is nowhere to upload to, which is also why there is no file size cap, no daily quota and no sign-up: processing costs nothing, so there is nothing to ration. You can confirm it in the Network tab of your developer tools in about ten seconds.