I have always done the ceiling and moulding in the same color, however, I have plaster cornice rather than wood moulding, and with plaster cornice there seems to have been two ways it was done originally (at least in my neighborhood): it matched the ceiling or it matched the wall color. I tend to like the crown and the ceiling to be the same white.

I always paint my ceiling a couple of shades lighter than the room and the crown is in a creamy white to match all of our other trim and doors. I'm not sure how it would work with coved ceilings, but saw a show the other day where they painted the room a chocolate brown and did the ceiling in a yellowish color, with white crown, it looked amazing.

Is there a reason to use a 'ceiling paint' vs. the cloud white color?

No. IMO ceiling white paint should be banned.

Get the cloud white in flat for the ceiling. There will be a difference between the crown and the ceiling because of this thing called flop angle. Plus, the different finishes, flat and semi will render the color appearance differently. The difference in finish and flop angle will indeed bring variety in how cloud white looks on the separate elements. However, it is still cloud white and despite the technical differences there will be a built-in harmony that you can pretty much count on. I would be comfortable just going for it, but you might want to sample before you buy gallons of anything.

If your crown is in semi, I would paint the door in semi too. Even if it were a spectacular quality paint, I'm not sure an eggshell finish in a color of white would last long around my house. In a situation where there is gentle use, it might not be an issue.

I painted all my woodwork and crown moulding BM White Dove - and the ceilings are 50% WHite Dove. I like the soft contrast and how the moulding still blends with the ceiling. Here are the pictures of my Family Room/Breakfast room to give you the general idea.

Here is a link that might be useful: Ceiling at 50% of Moulding Color

I'm with funcolors...ceiling white is an abomination!
In most rooms, an untinted white ceiling sits there over your head like a piece of posterboard, and makes you feel as though you were in a shoebox with the lid on.

In our previous house, I used a nice warm gray in our library, which had substantial crown and cabinetry in cream, and I painted the ceiling a very pale peachy pink. Not noticeable unless you looked at it, but it warmed the whole business up considerably. And I used eggshell finish, because I wanted a very subtle sheen in that room. Whenever the ceiling surface is in very good condition, I prefer eggshell...but it will make textures and flaws more noticeable.

Rooms with high ceilings and no crown look wonderful with the ceilings painted the same color as the walls (the height of the ceiling mitigates the flop angle). Pale pale blue can look lovely with camel colors. Green, I think, is always a little weird, because the sky is almost never green (unless you're about to take an unscheduled trip to Oz...). With green walls, a very subtle pale gold tint is nice. And if a white ceiling is desired, matching the trim color is the way to go. I usually choose cream ceilings with red or terracotta walls, because red is very reflective and will tint the ceiling with reflected light, and the yellow in the cream keeps it nice and warm.

I have BM Lily of the Valley semi-gloss on the crown and flat on the ceiling. Looks absolutely wonderful. Hate "ceiling white" which is what our painter always wants to do. I always win the argument-ha!

Thank you, thank you! I just needed someone, anyone, to say yes..you are on the right track. I will buy Cloud White in flat and start painting soon!