Windows expects icons in the ICO format. As the ICO file format reference explains, one ICO bundles several resolutions of the same image (16 x 16, 32 x 32, 48 x 48, and 256 x 256) so the operating system can pick the right one for each spot, from the taskbar to a desktop shortcut, an Explorer tile, or the Alt-Tab switcher. A JPG cannot store more than one size, and it has no alpha channel for transparency.

That difference matters the moment you try to use the image. People often assume they can convert image to icon on Windows just by changing the extension, but the file still has a JPEG header inside, not an icon directory, so Windows shows a broken or generic picture. If you ever need the reverse, you can turn an ICO back into a PNG for the web.

Both formats convert to ICO, but they start from different places. A PNG keeps an alpha channel, so a logo on a transparent background comes through clean. A JPG is always a solid rectangle, which is why a quick convert can leave a white box around the shape. If your art exists as a PNG, convert the PNG to ICO instead and skip the background step entirely.
The other factor is detail. JPEG is lossy, so a small or already-compressed JPG has little detail to spare when it is shrunk to 16 x 16. Start from the largest, sharpest version you have. When your only copy is a JPG and you want an alpha channel before you build the icon, you can convert it to PNG first, clean the background there, and then make the ICO.

The white box is the single most common complaint about JPG-to-ICO results. The icon shows up with a white square around it, because every pixel in a JPG has a color, including the background. Online tools that simply repackage the JPG carry that block straight into the ICO; ConvertICO even publishes a fix-it note on the white-background problem.

Icon Maker handles it in the editor. If the JPG has a plain white or solid-color background, you can clear that background and replace it with a transparent alpha channel before you save. For a photo or busy background, use the mask to erase or paint the areas that should be see-through. Either way the finished ICO carries a proper alpha channel, and Windows renders it correctly in Explorer, on the taskbar, and on the desktop.