@Tech Gig
1) For access from a remote server, your only option is JDBC. See link below for details.
https://cwiki.apache.org/confluence/display/Hive/HiveServer2+Clients#HiveServer2Clients-JDBC
2) Essentially, Hive Thrift Server is the same as HiveServer2. HiveServer2 uses the Thrift RPC protocol, hence the naming. The Thrift Client is is your Beeline or any client connecting to HiveServer2 through the Thrift RPC protocol.
For an explanation of the evolution of Hive from HiveServer1 to HiveServer2 (Thrift) take a look at the below link:
http://toodey.com/2015/07/25/what-is-beeline-in-latest-hiveserver2-difference-between-hiveserver1-an...
For info about HiveServer2 and Thrift RPC:
https://cwiki.apache.org/confluence/display/Hive/Setting+Up+HiveServer2#SettingUpHiveServer2-HiveSer...
For info on Beeline and other clients:
https://cwiki.apache.org/confluence/display/Hive/HiveServer2+Clients