There are several important differences between Microsoft 365 Personal and Microsoft Office Home & Student 2021:
Microsoft 365 Personal is a license for one year. This license can be used on a maximum of 5 different devices and also provides the possibility to work on your files online. It also includes one 1 TB of OneDrive storage.
Microsoft Office Home & Student 2021 is a license for an unlimited time and can only be installed on one device. This license does not include OneDrive, and you can only use the Office applications offline.
Both licenses will be linked to your Microsoft-account. This is why we recommend linking your license to a personal Microsoft-account, to guarantee continued access to your license.
You can find a complete overview of everything that is included on the product pages: