Gregorian chant is a particular style of plainchant that has become the norm for most of the Western Church. There are other styles of plainchant still in use; the next most common is Ambrosian chant (diocese of Milan), and to a lesser extent, Mozarabic chant (diocese of Toledo). Other forms have become defunct or nearly so: Benevantan chant, Gallican chant (which most closely resembles Gregorian), Sarum chant, and Old Roman chant to name a few. Not enough time (and not enough expertise on my part!) to go through all the differences, but suffices to say that there are definitive and major style differences between each form of plainchant.
Vernacular plainchant is obviously a very modern innovation, since the Mass in the vernacular on a wide scale is itself a modern innovation. But it is not “Gregorian” chant, it’s rather “Gregorian-inspired”, but for some languages can come very close. Oddly, some “Gregorian” chant in the Graduale Romanum isn’t Gregorian at all; apart from a couple of Ambrosian pieces that made it outside the diocese of Milan and into the Graduale, Mass VIII (de Angelis) that is so popular, isn’t actually Gregorian chant as it was composed many centuries later.
The major corpus of Gregorian chant was composed in the Carolingian era, around the 9th-12th century. But it eventually fell into disuse. It only regained “pride of place” in the Western liturgy sometime around the late 19th century, through the works of the monks of Solesmes. The culmination of that work was the release of the Vatican Edition of the Graduale Romanum in 1908. It forms the basis of the current (post-Vatican II) Graduale Romanum of 1974.
Not only is Gregorian chant more of a fairly recent revival as the “official” music of the liturgy, we actually have no idea if it sounds anything like the original compositions, which were written in free-form “neumes” without a staff. The square-note notation is often erroneously called “neumes” but in fact the true neumes are written without a staff. What we sing as Gregorian chant today is what the monks of Solesmes of the 19th century onwards tell us Gregorian chant probably sounded like (they are still at work to this day modifying melodies based on more recent research). It is no more, nor less “traditional” than the other forms of chant, alive or defunct, and it’s use as the main music of the Mass is in fact quite recent as until the monks of Solesmes, chant music for the Mass was a real mish-mash.
Plainchant, unlike polyphony, is sung to a single melodic line, all voices in unison. No single voice should dominate, and it is more free-form and un-metered (except for the hymns of the Divine Office which follow the poetic metre of the hymn).