Why do there appear to be two very different variations of “tongues” in the New Testament? The first variety seemed to be without need for interpretation because all those who heard it heard their own language being spoken.

Acts 2:8 (NKJV):


  And how is it that we hear, each in our own language in which we were born?


The second one the church is warned not to utter without interpretation. Paul said in 1 Corinthians 14:28 (NKJV):


  But if there is no interpreter, let him keep silent in church, and let him speak to himself and to God.


And in 14:23:


  Therefore if the whole church comes together in one place, and all speak with tongues, and there come in those who are uninformed or un-believers, will they not say that you are out of your mind?


What makes the initial event different from the subsequent?
In reference to the Acts passage:

The believers speaking in native tongues is a throwback to a Midrash on the Sinai event when the Law was received.  The rabbinic retelling has Israel speaking in all the tongues of the world, meaning that this is a monumental act of GOD happening.  The gospel is here, guided by the spirit and is intended for all peoples of the world, thereby undoing the judgement of the tower of babel.

The midrash is from Midrash Tanhuma 26c, as referenced in the book Speaking in tongues: the New Testament evidence in context.

And in respect to the Corinthians passages:

They are In respect to the spirit of GOD speaking through someone for the building up and edification of the local church and therefore not necessarily with the intention of evangelism.  The Corinthians used to fake speaking in tounges because they wanted to be seen as spiritual but here Paul is putting an end to that by saying don't speak in tongues in church unless there is an interpreter.

Craig keener, a Pentecostal evangelical conservative scholar has a great commentary on this called 1 + 2 Corinthians, it's totally worth the money.