Angels in Mormonism are either deceased humans or humans who have yet to be born. There is no strict classification of angels in Mormonism akin to the “Thrones, Dominions, Powers, Seraphim, Cherubim” etc. that Catholicism utilizes. Nevertheless Mormonism does recognize various “kinds” of angels without using a proper nomenclature to classify them.
First and foremost one could dichotomize all angels as either embodied or disembodied. Those who are embodied are either resurrected or translated humans (humans who have been made immortal by Heavenly Father without actually experiencing mortal death). The disembodied are those who either lived life and are now awaiting the resurrection or those who have yet to be born. Angel Moroni is in the former camp (embodied) and is believed to have been resurrected by God for the purposes of restoring the Church through Joseph Smith rather than having been translated from mortal life.
A couple other things to know about angels in Mormonism:
• Since Mormons believe that theres no substantial difference between humans and angels, all angels named in the Bible have been ascribed human counterparts in the Bible. For example, Mormonism teaches that the Archangel Michael is/was Adam. The angel Gabriel is/was Noah, etc.
• Because of this dichotomy between embodied/disembodied angels, Mormons are taught to test angelic visitation by offering their hand to shake. Resurrected beings from Heaven will oblige you and you’ll be able to physically shake their hands. Disembodied angels who are yet to be resurrected will ignore your request and will continue on with the message they were sent to give. Demonic angels (those 1/3 who rebelled against God and followed Lucifer to Hell) will never have a body but will still offer you their hand to shake. Doing so will result in you not feeling anything.
• Mormons do not believe in guardian angels (i.e. personal angels assigned to every human at birth who remain with them throughout life). Though it isn’t at all common for Mormons to use the term “guardian angel” I have in fact heard some Church members adopt the terminology very recently to describe the “promptings of the Holy Ghost” LDS members believe they have access to throughout their life after their confirmations. I only mention this as a cautionary tale should any uninformed Catholic run across a Mormon who says they do in fact believe in “Guardian Angels”. Again, I’ve only heard a handful of LDS co-opt the term, but given the LDS propensity to co-opt traditionally Christian terminology in order to subtly shoehorn LDS theology into a conversation I think it’s important to keep an eye out for such behavior.
If you should run into an LDS who insists that (s)he believes in guardian angels, ask them to explain what they mean. Either they’re co-opting the term or they genuinely believe in a concept that is foreign to their church (possibly a holdover from Christianity if they’re a convert).
• While the term ‘angel’ is almost always used in reference to angelic messengers, strictly speaking it isn’t wrong within a Mormon framework to refer to those humans who will never be exalted but aren’t destined to Outer Darkness (Mormon “Hell”). These individuals are believed to spend the rest of eternity as angels never progressing to godhood.