Two architectures, two risk profiles
Server-side. Your file is transmitted to a server, processed there and returned. A copy exists on infrastructure you cannot inspect, for a period you are taking on trust, accessible to whoever operates it and to anyone who obtains the URL.
Client-side. The page loads code that runs in your browser, and the file is read from disk into the tab's memory, processed, and written back. No copy exists anywhere else because none was ever transmitted.
Neither is automatically dishonest. Server-side processing has genuine advantages — heavier codecs, no device memory limits, formats a browser cannot handle. But it is a different relationship, and it should be a deliberate choice rather than something you discover afterwards.