When an EOS body starts, or when a card goes in, the camera reads the card's identity, mounts its file system, and finds the DCIM folder it will write to. Err 02 is raised when that fails: the card answered but its tables could not be read, or the card did not answer in time. A camera is less tolerant than a computer; a card a laptop will mount with a complaint may be a card the camera rejects outright, so the first thing to learn is what a computer reader shows. If the computer offers to format it too, the tables are torn; if the computer reads it cleanly, the fault is between the card and the camera.
The three options on the screen are the camera's, not yours. Reinsert powers the card again and asks again; it is harmless once, and a weak card is powered and asked each time. Change card gets the camera shooting on another card and leaves this one alone, which is the right thing for the camera and fine for the card. Format card with camera rewrites the file system, and Canon's note on its own error page says what that does to the images. Most Canon bodies' format is a quick one that leaves the data area alone, and a low-level format option on some bodies goes further; neither should be run on a card whose photographs are wanted. The bench rebuilds the tables on an image instead, and the files come back with their names where the entries survived and with their own dates where they did not.
The physical causes deserve a look before the card is blamed. SD contacts pick up grime and a wipe with a dry cloth restores a card the camera rejected; CompactFlash slots carry fifty pins and a bent one errors every card, and the camera needs a repair while the card is usually fine; a card with a cracked shell can still read on the bench. A card that errors in two bodies and a reader has failed, and its flash is read directly, through chips on a board or the test pads of a monolith.
Other makers word it their own way. Nikon's bodies report that the memory card cannot be used and may be damaged, and show CHA or CHR on the top plate; Sony's say they cannot recognise the memory card and ask whether to format; Fujifilm's show a card error; Panasonic's and OM System's say the same in fewer words. Each is the same fault with the same three causes and the same offer, and the offer is refused the same way.