Am I obligated to distinguish between morphs and megamorphs when I'm casting a card face-down?
As long as you make it clear that you are casting the card as a 2/2 face-down creature with no text, no name, no subtypes, and no mana cost, it doesn't matter what you say. The comprehensive rules aren't specific about what you can legally say, and the tournament rules only say that everyone has to be clear about what's going on.

When you cast a Megamorph creature, you are casting it as a Morph creature, so there is no need to distinguish. The Dragons of Tarkir release notes add this to the morph rules:


  702.36e Megamorph is a variant of the morph ability. “Megamorph [cost]” means “You may cast this card as a 2/2 face-down creature with no text, no name, no subtypes, and no mana cost by paying 3 rather than paying its mana cost” and “As this permanent is turned face up, put a +1/+1 counter on it if its megamorph cost was paid to turn it face up.” A megamorph cost is a morph cost.


In addition, as Jefromi points out, the Mechanics of Dragons of Tarkir says


  If you understand how morph works, megamorph is almost exactly the same. The only difference is that if you turn a face-down creature with megamorph face up by paying its megamorph cost, not only will it suddenly have its normal characteristics, but you'll put a +1/+1 counter on it as well!


Morph and Megamorph use the exact same wording for the bolded section, so you should just be able to say "I cast this face down" and pay {3}.