Difference between Ax 2012 and D365FO (AX 7)

Microsoft Dynamics 365FO (AX 7) is web-based and there is no separate client.

For development, Microsoft Dynamics 365FO (AX 7) uses Visual Studio (VS) IDE whereas the older version Ax 2012 uses MorphX. 

The other difference is Dynamics 365 for Operations is an introduction to Extensions. This extends the functionality of elements without overriding the existing ones.

The other main difference is the architecture.

Microsoft Dynamics AX 2012 different form styles are available where in Ax 7 Form patterns are introduced which makes development easier.

Another is the Introduction of data entities in Dynamics D365 Finance and Operations