Earlier quoted context omitted.
what postgresql, mysql etc. provide is a relational database, i.e. a way to store table-structured data with consistency and safety guarantees and efficiently perform operations to retrieve and update rows from it. sql is simply the standard language in which relational queries are expressed.
So the language implies something about the functionality of the database. That seems obvious enough. But does it necessaruly tell you anything about the underlying structure and the performance of a database? If we drop that acronym, "SQL", and still provide a database that handles relational queries (but perhaps uses a different but equally capable language), does that matter? If yes, how much? And why?
One of SQL's remaining powers over most other options is the ability of non-expert users to construct their own ad-hoc reports. This is a big part of why Hadoop has Hive, which incorporates a very SQL-like language, and most other "big data" tools have something similar.