"Nitpick: I see that sort of phraseology frequently from Orthodox on this forum. If the term "valid" isn't Orthodox, what term is? Please, let's at least learn to speak each others' language, here."
Orthodox resistance to using the term "valid" is primarily based on the RC practice of declaring certain sacraments by people outside the RCC to be "valid but irregular." This is most famously true of the concept of "valid orders" of vagante bishops whose "line of succession" is outside the Church...
The story was told of an Orthodox bishop who was approached by a Episcopalian priest at an ecumenical gathering early in the 20th c. The Episcopal priest asked the Orthodox bishop if he thought his orders were "valid."
The Orthodox bishop paused and asked the priest, "does your church consider your orders to be valid?" "Why, yes," the priest replied. The bishop's answer was simple: "then why would you need to ask me whether your orders are valid -- in what other church and under what other bishop would you want to exercise your orders other than your own?"
The only place where the nature of ceremonies done outside the Orthodox Church is any of our business is when someone is converting to Orthodoxy. Any other situation would involve great presumption in declaring *one way or the other* on what happens in non-Orthodox religious ceremonies.
As Coollidge nicely summarized, with additional good input from Kolokotronis and Kosta, there is a spectrum of opinion within Orthodoxy on the issues of how someone is received into the Orthodox Church. Most of the Orthodox Church tends towards caution in the first place, and I have observed a quiet trend, even in the more flexible American jurisdictions, toward a more strict practice of reception by baptism, blessing marriages by going through the Orthodox wedding ceremony, etc...
Now you ask: "You apparently make a distinction between "a Baptism" and "a ceremony that sort of resembles a Baptism, but isn't one" ... what is the Orthodox term for the latter?"
We call the one an Orthodox baptism. We don't presume to say anything about the other one. When one is received into Orthodoxy, the point is not what the person's former church didn't give him, but on the grace that the Orthodox Mysteries *do* give him.
This whole discussion, especially as it is going on between Latins and Orthodox, reminds me of some sound advice from +John of Kronstad:
"When the matter relates to God's Mysteries, do not inwardly ask: how can this be? You do not know how God created the world from nothing; you cannot and may not know here either how God mysteriously works. God's mystery must remain a mystery for you, because you are not God, and cannot know all that is known to the eternally Wise, Almighty God."
That is a very, very important (and correctly stated) point, Agrarian. Thank you. Ours is not to concern ourselves with those matters that are not Orthodox. We deal with the issues of the non-Orthodox only if and when they express a desire to become Orthodox, and then only for the sake of the spiritual wellbeing of the Catechumen.