It’s true of both books of The Well-Tempered Clavier that some preludes don’t quite seem to fit with the fugues they are paired with. For those that do appear connected, or at least bear some kind of family resemblance, the criteria one might use to characterize their relationship could range from detailed motivic and harmonic similarities, to simply an intuitive sense that they have both emanated from the same creative impulse, or have a shared inventio. There are little clues too, and sometimes they are the most revealing.
The subject of the first fugue from The Well-Tempered Clavier I shares aspects of contour with its prelude, though it may not be immediately apparent on the surface. By doing a voice-leading reduction of the prelude’s outer voices, the relationship becomes clearer:
This fugue has many notable elements—a small sample includes: the concentrated use of stretto throughout; that the subject appears at least once on each scale degree of C major; that the number 14 (B+A+C+H = 14) permeates both the surface and structure (e.g. the subject—if you are inclined to agree it ends on b. 3 of m. 2—consists of 14 notes; the piece consists of two large sections divided at m. 14; there are 14 entrances of the subject from m. 14 onward, etc.). But it’s relationships like those in the example above that, for me at least, glimpse most behind the veil.