Doctrine: A principle or body of principles presented for acceptance or belief, as by a religious, political, scientific, or philosophic group.
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Dogma:** A doctrine or a corpus of doctrines relating to matters such as morality and faith, set forth in an authoritative manner by a church. A dogma is that which is laid down with authority as indubitably true, especially a religious doctrine; as, the dogmas of the Church. Dogma rests on authority regarded as competent to decide and determine. Dogma has in our language acquired, to some extent, a repulsive sense, from its carrying with it the idea of undue authority or assumption. This is more fully the case with its derivatives dogmatical and dogmatism.
To answer your question, nothing, although we normally use dogmas in relation to religious institutions and doctrines to secular ones. The similarity is that both require a “compentant” authority to establish.