Salat might not be prayer. A better term for salat might be liturgy. Calm down. You can still call refer to salat as prayer. This is an academic discussion. So relax. But open your mind. Look at these definitions of liturgy and prayer.
Prayer is an invocation or act that seeks to activate a rapport with a deity, an object of worship, or a spiritual entity through deliberate communication. Prayer can be a form of religious practice, may be either individual or communal and take place in public or in private.
(My source is wikipedia. Deal with it.)
Based on my experience and my understanding of Islam, salat is liturgy and dua is prayer. Salat has a set time every day with much of the text of the service dictated by tradition. In that sense it is “customary.” Ideally, it is public. It can be done individually, but not only is there more merit in public performance, the very text of the prayer usually uses the first person plural “we” or “us” rather than “I” or “me.” Dua, on the other hand, can be done both privately and publicly without a significant difference in the merit of it.
Some might argue that this would make us sound like Christians, who also refer to their services as liturgy. I would counter that by saying “liturgy” is a neutral term used in the study of religion to describe practices within a wide variety of religions.
For the sake of compromise, it might be better to refer to salat as “liturgical prayer” or “canonical prayer.” Calling prayer “canonical” means that it follows an established tradition and that is certainly apt for salat. According to hadith, Rasulullah (S) learned the method of doing salat from Jibreel (A), the angel of revelation, known in the West as Gabriel. He taught it to his Companions and they passed it on in a chain that comes all the way down to Muslims of the 21st century. It is good to remember in salat that we are emulating all of our pious predecessors all the way back to Rasulullah (S) and Jibreel (A).