No. Tongues and 'praying in the spirit' are not synonymous. Let's look at some of the background:
Confounding factors for interpretation
The word 'tongues' is also the term used for 'languages', and so it can be difficult to interpret some New Testament passages. Most are clearly known human languages, but in cases like 1 Corinthians 14:15 Paul is clearly about a type of prayer where even he does not know what he is saying.
Church history is a complicating factor for interpretation. Very few early texts outside of the New Testament make any reference to 'tongues', and so we have very little material to go by for understanding these references in context. Similarly, 'tongues' has become such a widely known practice among some parts of the modern church that interpreters automatically assume this to be the same as the New Testament practices.
Many interpreters carry a silent assumption that Christianity has historically been the only setting 'glossolalia' happens, and so they assume it is de facto a divine practice or 'Holy Spirit' experience. However, tongues both predates Christianity and occurs in other religions and cultures, and so we need to factor this in when interpreting scripture.
Glossolalia as a Pagan practice
“Glossolalia is practiced among non-Christian religions: the Peyote cult among the North American Indians, the Haida Indians of the Pacific Northwest, Shamans in the Sudan, the Shango cult of the West Coast of Africa, the Shago cult in Trinidad, the Voodoo cult in Haiti, the Aborigines of South America and Australia, the Eskimos of the subarctic regions of North America and Asia, the Shamans in Greenland, the Dyaks of Borneo, the Zor cult of Ethiopia, the Siberian shamans, the Chaco Indians of South America, the Curanderos of the Andes, the Kinka in the African Sudan, the Thonga shamans of Africa, and the Tibetan monks.” George B. Cutten, An Ethnological Study of Glossalalia
Glossolalia is so widely attested among cultures relatively isolated from the middle-east that it becomes easy to see its widespread appeal and usage among pagans did not begin with the New Testament. Jesus himself attests to the practice:
*And when you pray, do not keep on babbling like pagans, for they think they will be heard because of their many words." (Matthew 6:7)
The pagans were well known for this behaviour.
Glossolalia as a Christian practice
In Acts, 'glossolalia' or tongues makes its first positive biblical appearance, and in each case the Christians appear to speak known, understandable human languages, which was a clear act of God. By contrast, every documented case in modern times has been heavily disputed.
After Acts, tongues rarely make an appearance, until the (arguably) most paganised church of the New Testament letters, Corinth. Here, Paul gives explicit and detailed guidance about tongues. The Corinthians had continued to use 'tongues' as a spiritual practice, and Paul affirms this as something which can be done to edify the soul. In the same way that the Holy Spirit takes a natural gifting in teaching or leadership and sanctifies it for use in the church, so too does he sanctify this pagan practice and make it acceptable for Christian worship.
Conclusion
In the passage in question, 1 Corinthians 14, Paul explains how this appropriation of the pagan practice can be personally edifying, but does nothing to help those around us:
6 Now, brothers and sisters, if I come to you and speak in tongues, what good will I be to you, unless I bring you some revelation or knowledge or prophecy or word of instruction? 7 Even in the case of lifeless things that make sounds, such as the pipe or harp, how will anyone know what tune is being played unless there is a distinction in the notes? 8 Again, if the trumpet does not sound a clear call, who will get ready for battle? 9 So it is with you. Unless you speak intelligible words with your tongue, how will anyone know what you are saying? You will just be speaking into the air. 10 Undoubtedly there are all sorts of languages in the world, yet none of them is without meaning. 11 If then I do not grasp the meaning of what someone is saying, I am a foreigner to the speaker, and the speaker is a foreigner to me. 12 So it is with you. Since you are eager for gifts of the Spirit, try to excel in those that build up the church.
13 For this reason the one who speaks in a tongue should pray that they may interpret what they say. 14 For if I pray in a tongue, my spirit prays, but my mind is unfruitful. 15 So what shall I do? I will pray with my spirit, but I will also pray with my understanding; I will sing with my spirit, but I will also sing with my understanding. 16 Otherwise when you are praising God in the Spirit, how can someone else, who is now put in the position of an inquirer, say “Amen” to your thanksgiving, since they do not know what you are saying?
Paul is providing a gentle correction to encourage the believers to only speak in languages they know and understand when in church. 'Praying in the spirit' is not a synonym for glossolalia.
In all three passages, I'd interpret 'pray[ing] in the [Holy] Spirit' to mean praying in conformance with or empowered by the work of the Holy Spirit. In Corinthians Paul is speaking into a very specific context and is being particularly specific by saying that it is possible to pray without consciously applying your mind to the prayer (and this is his explanation of the 'tongues' practice as used in churches). However as no such specific phraseology is applied in Judge or Ephesians, the natural reading would be to consider prayer as audible corporate prayer in a shared language.
