If you’re training by heart rate, I think that you need sport-specific heart rate zones.
For example, you mentioned that your heart rates are higher when cycling than when running. I have the opposite issue.
My guess is that, because less muscle mass is being used, the peripheral demands on the heart and lungs are less than in weight-bearing sports. But I’ve also found that lactate levels are typically higher, probably because less muscle mass is active and available to reabsorb lactate.
If your heart rates are higher than in weight-bearing sports, my guess is that your legs are relatively stronger than your cardiovascular system and/or the higher lactate levels of cycling are demanding more from your heart and lungs.
My two cents!