Hive was essentially a java library that kicks off MapReduce jobs. So the hive cli for example runs a full "server" in its client. If you have multiple clients all of them do their own SQL parsing/optimization etc.
In Hive1 there was a thrift server which was like a proxy server for this. So a thrift ( data serialization framework ) client could connect to it instead of doing all the computations locally.
All of that is not relevant anymore since Hiveserver2 has been the default for many years in all distributions and is a proper database server with concurrency/security/logging/workload management...
You still have the hive client available but this will be deprecated soon in favor of beeline which is a command line client that connects to hiveserver2 through jdbc. This is desirable since the hive cli punches a lot of holes into central hive administration.
So forget about hiveserver1 thrift server and thrift client.