How does running change your body?

I’m training for my first half and I’ve been enjoying reading posts here. In some, people comment about how running changed their bodies (shape wise). In the legs and waist line. Not sure if relevant but I’ve had 2 kids and don’t have a belly but my ab definitely looks different than before pregnancies.

I’m just wondering if I should watch out for something. I’m fairly skinny and don’t run for weight reasons. I’ve worked out my whole life and picked up running in 2017 and enjoy it a lot but this is my first time training for more than 10k.