What is the difference between supernatant and filtrate?

supernatant - liquid above and solid in the bottom, the supernatant is the liquid above that is going to be poured off (to separate the solid and the liquid)

filtrate - it is also the liquid part but the solid and liquid is separated differently, for example coffee the filter paper holds on to residue (solid) and the liquid part (filtrate) passes

I think that is the difference.