Head-to-head records usually combine every meeting between two clubs regardless of competition. Cup ties and league matches are different events, and blending them makes the record less informative rather than more.
Selection differs systematically
Domestic cup rounds are played in midweek between league fixtures, and clubs with congested calendars field changed teams as a matter of routine.
A cup meeting may therefore involve two elevens that would never start a league match together, with several academy or fringe players on each side.
Including that result in a record intended to describe how the two first teams match up imports evidence about a completely different pair of teams.
The stakes are asymmetric
For a smaller club, a cup tie against a larger one is a highlight of the season, prepared for over weeks and approached with maximum intensity.
For the larger club, the same fixture is an obstacle between two league matches, and the team selection reflects that ranking of priorities.
The resulting effort mismatch is real and specific to cup football. It does not carry over to a league fixture between the same clubs.
Knockout rules change the football
A cup tie must produce a winner, so a team that would happily take a point in the league has to keep pushing when the score is level.
Extra time and shootouts add outcomes that have no league equivalent, and a tie decided on penalties is often recorded in a head-to-head as a draw or a win depending on the source.
Two-legged formats introduce further distortion, since each leg is played with reference to the other rather than on its own terms.
Venue selection is not comparable
Cup draws are random, so the home team in a cup tie is not part of a balanced home-and-away arrangement the way a league fixture is.
A record that happens to include three cup ties at one club's ground overstates that club's advantage without any indication that it has done so.
League records at least have the virtue of alternating venues predictably, which makes them comparable across seasons.
How to separate them usefully
Keep league meetings, cup meetings and European meetings as distinct records, and read each against the competition it came from.
Cup records still say something, particularly about how a smaller club performs when it prepares specifically for a stronger opponent.
What they cannot do is contribute to a description of a routine league fixture, which is the context they are almost always quoted in.