This is one of those interesting questions which gets more complex (and harder to answer) the more you learn about it. Unfortunately I cannot answer definitively how theater projectors work. I'll explain why I don't think that question can be answered. And I'm going to reference 100fps.com a bit.
First, I don't think the question can be answered now, because projector hardware is kinda stuck. Look at how few screens in your area converted to 3D in the past few years. Yes, most theaters likely have 1 or 2 screens capable of 3D, but the expense of converting them all just isn't supportable. Because of costs like this, most theaters are using projection methods which are likely very out of date; so even if newer/better projection methods exist, it's likely you're still seeing older methods. But this question likely couldn't be answered in the past, because of different video standards. American cinema companies developed one set of film standards, while european companies developed another. This carries into broadcast encoding technologies for TV, and pretty much every corner of video.
One great bit of discussion can be found here. It looks at the question of how the human eye perceives video images, and some of the trade-offs necessary to make movies look fluid. Note in particular this observation:
The fact is that the human eye perceives the typical cinema film
motion as being fluid at about 18fps, because of its blurring.
This makes the main page at 100fps.com more relevant to the question of how cinema can get away with such low frame rates, as the main page is focused on interlacing (and image de-interlacing). Cinema blurs the images in each frame (by combining time slices) it gives the illusion of smoothness to motion.
As near as I can tell, most theaters in the US run at 24 frames per second, with 2 or 3 exposures per frame. The higher exposure rate prevents the eye from seeing the black shutter. The interlaced frames make the image look smooth. By comparison, most theaters in Europe show 25 frames per second, still with 2 or 3 exposures per frame. This low frame rate (by modern video game standards) works because the images are not crisply rendered computer images. So motion blur works to make it look better.
Some further reading: NTSC on Wikipedia, PAL on Wikipedia, Projectors:Shutter on Wikipedia, and the Flicker Fusion Threshold.