Move between JPG, PNG and WebP — to open a format something refuses, or to switch to one that keeps transparency.
Format conversion usually becomes necessary the moment something refuses to open. You saved an image from the web and it came down as WebP or AVIF that your photo viewer will not display. A form only accepts JPG. Or you need a transparent background and what you have is a JPG.
Formats differ in what they are able to carry. PNG and WebP can hold transparency; JPG cannot. Converting an image with transparent areas to JPG fills those areas with white, and that cannot be undone afterwards. You are warned on screen before that particular conversion runs.
On size, WebP is usually smallest, JPG next, PNG largest. Logos and diagrams with only a handful of colours can invert that ranking — PNG was designed for exactly that kind of picture.
Everything runs inside your browser. Because the image never reaches a server, we cannot store it or look at it. That difference matters when the file is company material or a personal photo.