Cookies and other ways of keeping a session upright are kept by the browser. So unless you're mad enough to copy cookies between devices, they prove you're on the same device.
Using a password every time you log in, and letting your browser wipe everything on shutdown does not show websites wether you're on yhe same or another device.
@Boomkop3@broken_chatbot Do you mean not keeping browser history actually makes big difference? I do that for few years but wasn't sure how much it really helped.