Lefty…I have to agree and disagree with Frank. I agree in that you are using the same muscles because it is the same body and all the muscles are being used, but you are using them differently. While you bike you are mostly seated, while you run you are mostly standing with a slight lean forward. The spine and body are at a different angle. After longer time in the saddle your base of your spine gets the crap beat out of it (all the way down to the coccyx and the hips with the ischial tuberosities -bone you feel when you sit), and if you are in the aerobars, your neck is held more perpendicular to the ground–whole different muscle strength needed to hold that up (why else would the RAAMers have to build devices to hold the head up where as ultra runners just need massage).
When you cylcle it is more up and down at an angle, when you run there is more rotation and freedom added into the process. Sprung pelvis is more likely to happen (and often happens) in a cyclist versus a runner. Shin splints are more likely to happen in a runner not a cyclist.
From the obvious–I know I am leaving out some important ones, just going off of a burnt memory right now…
Psoas and Hip Flexors ares more shortened when you cycle, elongated when you run.
ITB gets a little bit of a break more with cycling than running (angle of force and power of glutes) —but a weakness in the anatomical chain will put more force on the ITB to work harder–especially if the counter adductors are weak on the bike.
Hamstrings go through a significantly further stretch when you cycle (especially when you are in the aerobars) both activities can tear the hamstring from the ischial tuberosity -enjoyable sensation, and recovery blows. Squats/lunges/stairclimbs will help build these (lower weight higher reps–not the heavy stuff) kind of simultating being on the bike and climbing a hill.
Quads get abused in both like the hams, but angle plays a huge factor. If you sit for a long time the quads aren’t getting stretched out enough at the origin (up at the top) and the attachment down under the knee (of the rectus femoris) can take a beating from being over powered. When you cycle you are stuck in a position, when you run the pounding is different and more open to injury (adjustments from rolls, ect).
Low back muscles are worked different because of bending in aerobars and of course the abs --those just better be strong no matter what. Quadratus lumborum fibers are more taxed from being in the aerobars and more rotational when running.
Calves and counter anterior tib and peroneus muscles just get abused. On the bike you are less likely to feel the ache/pain because you are on a machine, on the ground, you get a cramp, nothing to compensate and you are going down.
Neurological weaknesses/impingements can mess you up with being able to lift your foot which you will notice more on the run than the bike, because once again you are clipped in on the bike. On the run, not being able to get foot clearance you will be on your face before you know it.
Piriformis just gets beat up ugly on both. Sitting is worse on the piriformis but long term pounding can shut down the butt too.Don’t forget to strengthen your anterior tib (pumping the gas pedal motion) because often the calf muscles are so strong.
LATTS!!! Be sure these babies are strong. The muscle has fibers that attach to your sacrum and courses in front to the front of the arm–very powerful muscle needed. Usually more outstretched in the aerobars and the power is actually used when you run.
The easy answer is all around fitness
adding in Pilates/Yoga to help with flexability. There is more, but those muscles are the keys to address.