Hive Services

• HiveServer2
• Hive Metastore
• HCatalog
• Beeline & Hive CLI
• Thrift client
• FileSystem :: HDFS and other compatible filesystems like S3
• Execution engine :: MapReduce, Tez, Spark
• Hive Web UI (added in Hive 2.x). Maybe also Tez or Spark UI, but not really

Driver

The JDBC/ODBC or Thrift interfaces have drivers.
There are also the processes that interpret the query and compile it down to the execution engine code. I personally call that an interpreter or compiler, not a driver

Metastore Server

Not part of HiveServer2, and not a JVM process (except for Derby). It is literally a RDBMS (yes, you still need these when running Hive & Hadoop).

Supported Remote Metastore servers = Oracle, MySQL, Postgres
Embedded Metastore (not recommended for production) = Derby

See Hive Wiki

Metastore JVM

The orange boxes are showing you can deploy these services as part of the same JVM as the driver (interpreter) or as a remote server. The wiki describes these setups.

I believe this is a side-car process that maps the HiveServer2 queries to the MetaStore queries. For example, how do you translate the HiveQL into a process that reads metadata from MySQL or Postgres?

It can run on the server-side, yes, but this is not a recommended setup for fault tolerance and performance reasons.

HiveServer1 is deprecated. Feel free to read about it, but don't use it.