I was getting pretty confused with the various options around powershell commands to use with Exchange online.  For example, to add a user to a distribution group in O365, I had come across 4 different commands:

So after some digging I realised that the *-AzureRM* are powershell cmdlets to modify general Azure resources using the Azure Resource Manager model – read more here (first couple of links are most useful)

Furthermore, the current way to manipulate Azure AD is to use the V2 cmdlets:  *-AzureAD* read more here 

The older *MSOL* cmdlets have been completely replaced by the *-azureAD* cmdlets.  Although the older cmdlets still work, they have been marked as deprecated so at some point they will stop but that might not be for a while. Read more here.

The Add-DistributionGroupMember cmdlet applies to Exchange and Exchange Online.  Given that Microsoft haven’t given any indication that they are likely to remove support for hybrid environments it is likely these will be around for a while.