It's worth to say that both tags were used together in several questions. There are 85 questions double tagged this way while there are 159 questions with google-apps-email tag Vs. 2591 questions with gmail tag
As a Web Application there are very few differences but most of them doesn't change the UI or the change have minimum impact and it's explained in the Gmail Help so in for both tags the source form many questions is the same.
In Gmail for Work (one of the names that Google use to call Gmail edition for Google Apps)
- Custom logo instead of the Gmail logo
- Slight different tab names for only one tab.
- Few features could be blocked by the organization administrator