Microsoft Access 2013 is the software that has progressed over the ages from Access 1.1 in 1992 until now.
Office Professional 2013 Software (which includes Word, Excel, PowerPoint, Outlook and Access) will allow you to install and run Access 2013 as usual.
The Office 365 version is paid by monthly subscription and provides Web services to Office 2013. It includes the Office Professional 2013 software as well as Access 365 and Access 2013.
Access 365, besides the name “Access”, has little to nothing in common with Access 2013 or previous versions of Access.