The service and the desktop Acrobat DC subscription are tied to your Adobe ID. If you use the same ID, the subscription applies to both.
If your Acrobat DC is not a subscription, it's a curious thing - Adobe don't call this Acrobat DC. They call it Acrobat 2015, Acrobat 2017 or Acrobat 2020. Because you don't pay a subscription in this case, you also don't get any online service.