The Personal accounts (also called Microsoft accounts/IDs or Live IDs) are the ones you as an individual create directly with Microsoft. The prime example would be people who've had a Hotmail account for ages, and that eventually became a Microsoft account.
The confusion comes because since a couple years ago, you can create Microsoft accounts with any e-mail that you own, be it personal, from work, hosted in gmail, hosted by your employer, hosted by yourself... You name it. So it is possible to create a Microsoft account with your work e-mail, even if your work e-mail also has a Work/School Account tied to it. All the notifications for that Microsoft account will go there, but they are not for your "Work/School Account" (also referred to as Organizational account), they are for your personal one.
Yes, it is a mess. After a while I got used to it and now I'm comfortable navigating all my identities, but it can be very annoying when you first encounter it.
