In terms of differences with Christian denominations these are over more minor doctrines, or really over largely the question of authority. This is why the 3 points listed in Post #4 (Jesus life as explained in the Apostle's Creed, the trinity doctrine describing God as explained in the Athanasian Creed, and holding the Bible as the divinely inspired religious text of Christianity) are really the main unifier and way to distinguish a legitimate Christian denomination from either a pagan religion or a heretical sect. All valid Christians are unified as a whole Christian religion in that they hold the 3 beliefs listed.
A 4th perhaps side point that is sometimes made is that a valid denomination should have a historical link to the apostolic succession as well to distinguish it from a more modern cult or a passing movement that comes and goes in the course of history. The historical link to the apostolic succession gives a sort of objective chain from the apostles in the Bible to the modern day as opposed to a newfound and questionable denomination that claims to have some new revelation to try to justify them bringing a different gospel typically to the worldly benefit of one person (a cult leader) or a group of people or political movement. Though one could even consider this something of a moot point since most newfound denominations that do not have a historical link to the apostles also tend to reject one or more of the three core beliefs of Christianity and therefore they could be considerred wholly different religions or elsewise heretical to the point of being outside of the unity of Christianity (ie: islam, jehovah's witnesses, mormonism, etc.)
A 4th perhaps side point that is sometimes made is that a valid denomination should have a historical link to the apostolic succession as well to distinguish it from a more modern cult or a passing movement that comes and goes in the course of history. The historical link to the apostolic succession gives a sort of objective chain from the apostles in the Bible to the modern day as opposed to a newfound and questionable denomination that claims to have some new revelation to try to justify them bringing a different gospel typically to the worldly benefit of one person (a cult leader) or a group of people or political movement. Though one could even consider this something of a moot point since most newfound denominations that do not have a historical link to the apostles also tend to reject one or more of the three core beliefs of Christianity and therefore they could be considerred wholly different religions or elsewise heretical to the point of being outside of the unity of Christianity (ie: islam, jehovah's witnesses, mormonism, etc.)