Gabriel, Michael belongs to which type?
Gabriel, Michael, Raphael, and Uriel are four angels which are traditionally recognized as being chief-angels, aka archangels. Only Gabriel and Michael are mentioned in the Tanakh/Protestant Old Testament, Raphael is mentioned in Tobit, one of the Deuterocanonical books, and Uriel is mentioned in 2 Esdras* (also called 4 Esdras or Latin Ezra) an apocryphal work that is only really found in appendices in some medieval copies of the Vulgate.
*The naming of the books of Esdras is complicated. The Tanakh (Jewish Bible) only has one book, Ezra (in Greek, Esdras). The book was in Christian Bibles split into two, and called 1 Esdras and 2 Esdras; then in Protestant English Bibles 1 and 2 Esdras became Ezra and Nehemiah. And then the other books of Esdras (3 and 4 Esdras) then became known as 1 and 2 Esdras after 1 and 2 Esdras became Ezra and Nehemiah.
After the rebuilding the Temple when the Jews returned from the Babylonian captivity we enter into a period of Jewish history known as the Second Temple Period, which lasted until the destruction of the 2nd Temple in 70 AD. During this time there is a lot that got written, including a number of books of the Old Testament as well as most of the New Testament. A lot of these works would never be received as Scripture by Jews or Christians, but they were still influential in various ways, such as the several books which make up the "Book of Enoch", which is actually quoted directly in the Epistle of St. Jude in the New Testament. While not Scripture, and therefore not divinely inspired, they were still historically and culturally significant, and informed both Jewish and Christian thinking to varying degrees--including the names of different angels.
Generally speaking, we only see the names of angels at all in Post-Exile, Second Temple Judaism--prior to the Babylonian Exile angels are nameless. Which is why we don't see Gabriel and Michael mentioned until the book of Daniel, and then also mentioned again in the New Testament.
So while the Bible, depending on who you ask, only mentions 2-3 angels by name (all identified as chief or arch-angels in Judaism and Christainity), both Jewish and Christian tradition have always recognized many archangels, usually at least seven--though only the "Big Four" of Gabriel, Michael, Raphael, and Uriel are common in all traditional lists of archangels.
Which is kind of why I said that such things really don't matter, and there's no angelic bestiary, there's no authoritative, definitive list of types of angels, or names of angels. We really shouldn't even be all that interested in that because it's probably at best only a distraction. The angels do their thing, and we do ours.
-CryptoLutheran