Many runners prefer bone-conduction headphones for running as those leave the ears uncovered and the person more aware of their surroundings. For the same reason, these headphones might not be the most ideal in noisy environments since they let in too much ambient noise, making it hard to hear what's being played in the headphones.
Running headphones with ambient mode are a good alternative as these buds often also have active noise cancelling (ANC). When the ambient mode is turned on, the earbuds use their microphones to feedback sound from the outside world so that you're more aware. When running indoors – e.g. on a treadmill – you can activate ANC and block out sound, so you can get in the zone easier.