Sorry for the delay, Tamara.
Strictly speaking, ‘orthodox’ means ‘right-praise’; thus also means praising correctly. It’s a term of practical theology, in that most anyone bothering to worship religiously (some religions don’t have, or don’t necessarily have, ‘worship’ of the deity, of course) will want to aim their worship correctly, so to speak. This is also related to the idea of wanting to claim correct instead of incorrect things about the deity.
In that sense, all honest persons believe he or she is being ‘orthodox’ insofar as they think they have at least some correct ideas about the deity (even if they don’t worship deity per se). Even an atheist who is honestly thinking he is correct about God not existing, is being ‘orthodox’ in that fashion; if he is correct, it is all theists of any stripe who are in error–or, going back to the Greek word behind our term ‘error’, are in ‘heresy’. (This should be distinguished from a sin of ‘heresy’, which even an atheist could in principle acknowledge, where a person intentionally propagates what they themselves do not believe to be true in order to gain some benefit for themselves thereby. Such a sin can in principle be extended to those who misuse actual truth for their own selfish ends, too. So, even an atheist could in principle accuse a televangelist making himself rich off his hypocritical exploitation of other people’s theism, of committing the sin of heresy; or could accuse a popularistic atheist of doing the same thing. It is not uncommon, in my experience, for modern atheists to deride and reject the atheistic political regimes of communist dictators in terms which indicate that the dictators are being accused of ‘the sin of heresy’, though that phrase isn’t normally used, of course.)
For purposes of classifying and identifying ideas in shorthand, however, during religious discussions about Christianity, it’s pretty typical to use the term ‘orthodox’ to refer to a particular majority party (which itself has divisions, of course, like Roman Catholic and Eastern Orthodox and Southern Baptist) which accepts (though sometimes in various ways) the doctrines of the Apostle’s Creed, the Nicean Creed and at least the trinitarian faith statement of the so-called Athanasian Creed.
This is how I usually use the term myself. I don’t thereby mean that those people (including myself) are necessarily correct.
An adoptionist, by sociological contrast to the ‘orthodox’ party, rejects the idea that Jesus Christ was always God, and instead promotes one of several various ideas that (put a little roughly) God only ‘adopted’ Jesus as a son at some point in the life of the man Jesus of Nazareth. The most common adoptionist idea is that God only first adopted Jesus during the descent of the Holy Spirit at Jesus’ baptism; though even then there are various distinctions among that kind of adoptionist: did the 2nd Person of the Trinity begin existing in and along with Jesus at that time?–and was that 2nd Person the Son instead of the Holy Spirit, or was that 2nd Person the Holy Spirit with the man Jesus being the Son?–or did the one and only person of God (i.e. God the Father) begin living in and working directly with and through Jesus at that time?
There are (or have been, or could be) various ‘adoptionist’ Christian groups going any of those directions; as well as adoptionists who believe and teach that God adopted Jesus at birth, or at conception, or at the resurrection, or even at Jesus’ ascension. None of those groups are simply pulling their ideas out of thin air; they all have at least some amount of metaphysical plausibility to them, and they all have at least some amount of scriptural testimony to appeal to.
And each group would consider itself orthodox, not in the sociological group-identification sense, but in the far more important sense of trying to give correct worship to, and correct proclamation of, God.
(Meanwhile: mental note that I still haven’t written an essay addressing Jeff’s question! yeesh… Definitely another entry, or whole set of them, for the two trinitarian crit threads. Someday. When I can finally get around to it. I’ll link to it from here whenever I do, though.)