Why a tool that runs in your browser is more private
Most online converters do the same thing: your file travels to a server, is processed there and comes back. It works, and it also means a copy of your document existed on someone else's computer.
What an upload really involves
Uploading means your document is written to disk on a machine you do not control, passes through whatever software is installed there, and is kept until a cleanup job removes it. Serious services delete files within a few hours and say so in their policy; you are trusting that they do.
For a holiday photo it hardly matters. For a payslip, a medical report, a contract with names and figures, or a document covered by a confidentiality clause at work, it is a decision you should take on purpose rather than by habit.
What changes when the work happens on your device
Modern browsers can do this work themselves. The page downloads the code — the same open-source engines a desktop program uses, compiled to run in the browser — and that code reads your file in your computer's memory, processes it there and hands you back a download.
The document never travels. There is nothing to delete afterwards on anyone's server, nothing to leak in a breach and nobody to trust about retention. It also means no queue and no upload wait: on a big file, the slow part of an online converter is usually your own upload speed.
The trade-off is honest: the work uses your device's memory and processor, so a very large file on an old phone can be slow, and some things — anything that needs a font you do not have installed, for instance — simply cannot be done locally.
How to tell which one you are using
Open the browser's developer tools (F12), go to the network panel and convert a small file. If you see a request uploading several megabytes, your file left. If the traffic is only the page's own code, it did not.
Another clue: a tool that works offline is working locally. Load the page, turn off the network and try again — if it still converts, nothing was being sent.
Read the privacy policy for one specific thing: not whether they promise to delete files, but whether the files are sent at all. Those are very different statements.
What a local tool still cannot hide
Your visit to the site is still a visit: the host sees the request for the page, your IP address and your browser, the same as any other website. What it does not see is the content of your file.
If a page shows advertising, the ad network sees the visit too, not your document. CLEKARA explains exactly this in its privacy policy, and every tool page says what the tool does with your file.
Being able to check it matters more than being told. That is why it is worth using tools that let you verify, with the network panel open, that nothing was uploaded.