Hi,
Microsoft Office Home and Student is a package where you can purchase for one-time payment. It only includes Word, Excel, PowerPoint and OneNote. Office 365 Home and Personal which is a subscription type, includes all Office applications such as Publisher, Access, Word, Excel, PowerPoint, OneNote and Outlook.
However, since you prefer a bundle that came with Publisher, you may want to purchase Office Professional 2016that includes Outlook, Word, Excel, PowerPoint, OneNote, Access and Publisher.
You can also check the information about Office suites on this link.
Let us know if you need further assistance.