"Correct" storage. Position the jack mechanism so that its near the middle of the jack "column". One end of the column fits into that angle that's visible in the upper corner of your first photo. The jack mechanism should be positioned so that it will be held down by the tire. The hooked end of the bolt goes into that bracket and up through the center of the spare. The jack foot place goes upside down onto the spare (which is also 'upside down' - brake side up) with the stem of the bolt also going through the jack foot plate --- everything held down by the big wing nut. There's also supposed to be a piece of rubber on the jack column that the lug wrench slides into.
Yeah, from your second set of photos, you've got the wrong jack. The column is too long to fit where it's supposed to.