Is either account currently under a discount plan? That’d be the first year of something like a “Free First Year” type of plan. Not that they offer Free, but close to it at times. You can’t migrate hosted sites to one of those plans.
The DIY approach would be to back up that 1 Website on the first account. And its database(s) if it has any. You didn’t mention anything about email accounts. Once the site is completely backed up, delete it from the system and recreate it in the other account. It may take several hours for the old site info to clear from the system, thus allowing you to set up its duplicate in the new account.
The non-DIY approach is to ask Support, which you may have to do if DIY doesn’t work/clear out. You should still back up your site just to be safe, then submit a request to Support to move the files over. They might do this as a courtesy.
For that 1 Domain, I’ll assume it’s just a registration. You can do that yourself at any point. Just initiate a domain transfer. You’ll pay the $9.95 registration, but that adds one year to the existing registration, so you don’t lose any time on that one.