Managed Metadata Service and Local vs Global Term Store in SPO

Could someone please explain the concept of the MMS in SPO?  In the https://technet.microsoft.com/en-us/library/sharepoint-online-content-service-description.aspx it mentions that MMS is one of the services provided.  Does this mean that all site collections "subscribe" to the MMS automatically and share a term store at the tenant level? And if we wanted to use a local term set, we would have to select 'customize your term set' under the Term Set settings for the Managed Metadata site or list column?