Difference between an Azure AD "directory" and an Azure AD "tenant"?
I don't have enough rep to comment on the other answer, but the comment "You can have multiple AAD directories assigned to a single subscription." is not correct per the documentation, rather the opposite. https://docs.microsoft.com/en-us/azure/active-directory/active-directory-how-subscriptions-associated-directory
Multiple subscriptions can trust the same directory, but each subscription trusts only one directory.
My understanding is that "tenant" and "directory" are basically used interchangeably in the Active Directory documentation. I think it's just more convenient to use "tenant" sometimes since the title of the service is "Active Directory" so referring to an "Active Directory directory", for example, would be confusing.
You are correct, in order to use Azure AD you must become a "tenant" within the system. So a tenant is basically just securing a .onmicrosoft.com sub-domain. At that point you would have one account registered in your Azure AD. From there, you can activate Office365, Intune or any of the Azure services.