Most digital cameras recommend that you format the card only on the camera - my current Pentax X90 included. If you use a cable to download photos, you can generally pull the plug when the process is finished. If you remove the card from the camera and connect it directly, it's much safer (and often essential) to use 'Safely remove'.

Re the xD cards used in some Olympus/Fuji cameras - this was a format jointly developed by Olympus & Fuji and they both made cards. They are considerably smaller than SD cards. My Olympus camera had a couple of features (panoramic stitching was one) that worked if I used an Olympus-branded card, but not with a Fuji-branded card.

Phil