This is a question we sometimes receive. You have one website (maybe only presentation) available at mycoolbusiness.com and a shop subdomain at shop.mycoolbusiness.com or mobile version at m.mycoolbusiness.com
For any of these cases you will only need a single account to manage all these. You only need to register with the root domain (mycoolbusiness.com) and just make sure the integration code is added to any webpage on this one as well as subdomains.
Technically there are some limitation of how browsers work (for example you can’t have conditions from both subdomain and main domain) in a single campaign. But the main benefit, of having users identified across domains it’s achieved.