The syntax in this Blog is focused on Multi-Tenant environments. Anyway you can use most CMDlets on an OnPremise Exchange Server as well. Here some syntax examples :
Syntax for MultiTenant Exchange 2013 / 2016 server :
Get-Mailbox -OrganizationalUnit “TenantName” -Identity “Mailboxname” | ft
Syntax for MultiTenant / Hosted Exchange 2010 server :
Get-Mailbox -Organization “TenantName” -Identity “Mailboxname” | ft
Syntax for OnPremis Exchange 2010 /2013 / 2016 server :
Get-Mailbox “Mailboxname” or -Identity “Mailboxname”
Multi Tenancy is explained in the following TechNet link by Microsoft :
Multi-Tenancy in Exchange 2013
