Yes. That's always how I hear and use them, or almost always.
The 'carry out' may be for both, a little more ordering side.
'To go' pretty much all business.

My guess is that there has taken place in the food service industry an effort to phase out "take-out" in favor of "pick-up" when it comes to phone orders. When you place your order at a restaurant, it makes sense to say "take-out" or "to-go." It would not only sound odd but be incorrect to say “for pick-up" at the restaurant because "for pick-up" connotes a future act—but you're already there. When you order over the phone, it makes sense to say it's "for pick-up" because you'll be coming later to get your order. I'm also in Milwaukee, and I think that in the past it was much more common to say "for take-out" when phoning in an order—and it was understood. I suspect that "the industry" has internally promoted "pick-up" as a way to distinguish between phone orders and counter orders. However, restaurants that you call and pick-up your order at are, by and large, still called "take-out" places. Are they to become "pick-up" places? You're looking for some kung pao, not a one-nighter!