Microgrid is a loaded term, there are a lot of things that it can be, and a few things that it isn't.
To me, there are a couple of things that a microgrid MUST have.
1 Generation
For a discrete system to be called a microgrid it MUST have some form of generation, just disconnecting from the grid and running on storage is not enough.
Typically the generation has been diesel generators, but with the cost of solar dropping so quickly, a lot of research and pilot projects in using solar as the backup generation source.
2 Interconnection protection and controls
What this means is that a microgrid shall be able to disconnect and re-connect to the grid automatically. This means that an operator should be able to give a signal and the microgrid will be able to disconnect from the system without dropping any load, and then re-connect to the grid at a later time without a disturbing the system.
That's it
If the system has these two things, I think you can call it a microgrid. If you are only connecting/disconnecting generation, this would be called distributed generation or DG.
If you add storage to the mix it can help ensure the stability of the microgrid in a lot of different ways.