I have been in the Charismatic Renewal for over 40 years now. I have sat under and taught many Scripture Studies on the Gifts of the Holy Spirit.
Scripture talks about 3 and variations of those 3 kinds of tongues.
1st is the gift of tongues as given at Pentecost. This type of tongues are the ones where a person speaks in a tongue of a known language although totally unknown to the speaker. I have seen this gift in action several times. The speakers I witnessed spoke in an Indian (India) language, one in a Chinese dialect, one in Old Gaelic. My friend tells me of a person speaking in an African Tribal language and an old woman from Africa being present to hear and understand. Each of these tongues were Praising the Holy Trinity.
2nd is the Tongue that requires an interpreter. In my experience, this is the rarest of tongue gifts. I have seen this gift only a few times and one time I had the gift of "interpretation" but didn't speak it out but someone else did, speaking exactly the Words I heard in my Spirit. There was a time in Southern Calfornia during a Prayer Meeting when a van load of Down Syndrom adults was brought. These were severe cases, some in wheel chairs and most could not speak much at all. However, in the Spirit they were Speaking in tongues and Interpreting perfectly clearly. They were exhibiting many of the "Word" gifts, including the gift of the Word of Knowledge and Prophesy. I have to tell you that we, including a Catholic Charismatic Priest were stunned by this show of the Power of the Holy Spirit. Every word spoken could be tested against scripture and be found solid.
The 3rd type is what we call our "prayer language". Scripture says when we do not know how to pray, the Spirit will pray through and for us. This is the most common form of the Gift of tongues. We praise God in tongues when we simply run out of words in our own language. We also sing in tongues of Praise and Worship.
We look for the Fruits. That will be the first sign that they are from God.
As I mentioned there are variations of these three tongues and I think that may be why some Christians claim there are 4 types. However, I am very open to hearing more about the fourth one.
Blessings