When you use SQLPlus and make a bequeath connection (e.g., not going through the listener and not specifying the SID/Service Name in the connect string or using a TNS alias), SQLPlus/Oracle uses the combination of ORACLE_SID and ORACLE_HOME to uniquely identify the instance that it connects to.
Important to note: You may have multiple instances running on one server which all share the same OH, but they will have different SIDs. Or you could have multiple instances running from multiple Oracle Homes. Two instances on one machine will never share the same combination of SID and OH.
It's important to note that this connection method will only work when you're making connections from the command line of the server that the Oracle database/listener is running on.
If you're connecting from a remote server (or from the same server if you need to connect to a specific service - e.g. a PDB in 12c), you must specify in the connect string one of either a tnsnames alias, or the hostname [optional: port] and the service name you're connecting to.
This assumes the tnsnames.ora on the client is set up with an alias for "hr". This TNS alias will have the hostname, port, and SID/Service Name in it.
This connects to the hostname and SID/Service Name provided on the command line. ORACLE_SID, ORACLE_HOME variables and TNS are entirely unrelated to this connection and are not used.
A real example:
sqlplus hr/[email protected]:1521/hrdb