Can you provide context about how you're "connecting" the databases? SQL Express is a database engine as is SQL Enterprise edition. One way to "connect" them would be to use linked servers. In that regard you can link to servers of differing instances without issue. But I'm struggling to understand a context where you'd be using SQL Express to access SQL Enterprise databases. It would make more sense to just directly connect to the Enterprise instance.
Can you provide the reference that "told" you the information you're reporting? If it is docs that would be useful. If it was a person then perhaps you should ask them where their information came from.
Where are you seeing "Database Services" being used? The database engine is the thing that holds the databases and provides access to them. A database service could be the myriad of services a database product may provide such as reporting, integration, logging, etc. Without the context it is hard to say what it means.
Finally, note that just because you can "connect" doesn't mean it is legal. In order to access an Enterprise database you must have a CAL for it. It depends on what licensing model you're using but frequently each user must have their own CAL to access the database. Hence using SQL Express to connect to SQL Enterprise still requires a CAL for the user accessing the SQL Express instance even though SQL Express itself doesn't require one.