Ruth Kulerman
Sorry, I was just asked to respond to questions that interested me. So although this answer is delayed, please know that yes, I found the question interesting. Here is an Irish stew of an answer (An Irish stew has lots of stuff in it!)
I once created a phrase to cover all auditioning situations
--a phrase not exactly inspired but pathetically accurate:
"Minefields, Quicksand, and Murphy’s Law of AUDITIONING."
Which is to say, almost everything in the world can happen at an audition. Cameras fail, coffee spills, your "sides" are mysteriously out of numerical order, cell phones (yours or theirs) break all moods, they cough, you cough, a fire engine races down the hall outside your auditioning room--anything anything anything can and will happen. Handle it all with grace and if possible with a touch of humor.
But the following is sort of, nearly, perhaps, almost what you might expect to happen:
1. Feature film, major studio, tiny role: Quite often a prelim "chat." They want to "sense" you. Questions I have been asked so they can break the ice? 1. What was it like working with____(a huge name director)? How was it playing a lesbian? How do you think you should treat ____ (the name of a HUGE star in the film)? How do you see yourself?
2. After the chat, you will probably read on camera--your partner might be a hired actor trying to impress the casting director, might be a wonderful actor who feeds you more than you could possibly expect, the casting director, or the coffee gofer. If you have a tiny role and have had the sides a couple of days, yes have the lines learned but hold the sides in your hand. (How to hold sides is a whole other lesson!) Preparation of script and preparation of yourself in the auditioning situation are the best ways to ward off jitters.
3. Student film--maybe cold reading of sides. Maybe a monologue. Try to use a monologue that is somewhat appropriate for the role you want. Maybe prepared sides. Maybe a short chat. Maybe student directors who are utterly professional. Maybe student directors who are disorganized or as nervous as you are.
4. Extra work? That is mostly type. It is a great way to learn what working on a film is like. Watch, listen, network. Competition? Anyone who is there! Being chosen depends on what the extras are being used for.
5. How to beat the competition? Ah that answer is an entire book. But in extra work mostly it depends on your attitude and appearance. In small roles, a lot depends on your type, your attitude, your professionalism, your confidence and then on whether you can deliver the lines believably.
Whatever happens at an audition, keep your good manners, lock impatience in a drawer and leave it home. Expect lots of wasted time. Be grateful if you are in and out in an hour. Do not complain or whine. Leave if you are starting to boil. Better a "no show" than a "bad show."
Just keep on self-submitting for everything possible, keep going to open calls, keep learning how to audition. There really is nothing more thrilling than doing a scene as a principal or as an extra in a film --student or major studio.
Expect anything to happen. It probably will. Murphy's law of auditioning.

I'll go ahead and answer this myself since no one bothered to help. I just got back from aforementioned audition. Other hopefuls were there, we waited outside the audition room together, then I was called in individually and ran the short scene a few times with the casting director while she videotaped it.

The biggest difference between film and stage auditions is that I was expected to have my scene and lines memorized (the casting director had emailed me earlier to tell me the part she wanted me to read for, and the script was online).