It's the same thing. Don't be a jerk about it, but do speak up. Remember also that if you decide to buy that new boat after all, and put off the whole CD project until next year, you are responsible for paying the designer for any work she's done to that point. Ask for a final invoice and pay it. There are a couple of ways to get the finished design out of the computer and onto ink and paper.
Film is what the printer uses to put ink onto paper.
The reason I like to give the disk straight to the printer, and not use a service bureau at all, is that it keeps all the responsibility in one place. The printer can't blame the film for anything, since the printer is the one who output the film in the first place. Any problem is either with the designer or with the printer, and whoever is at fault is responsible for fixing it. In Los Angeles, I don't know of any printers who don't have computer capabilities. There's a complicated physics explanation for why these four colors are used, which has to do with their complimentary relationships to the primary colors of light, but you don't need to worry about that and, frankly, neither does your designer.