There isn't usually a Ballet Master assigned to a specific production -- the Ballet Master is the head teacher at a ballet company, who is in charge of running daily dance classes and running rehearsals for whatever productions the company is doing. She works with the company's Artistic Director to decide on how far and fast to push the dancers in class, what kind of styles they want to focus on teaching, what skills need to be refined for upcoming works, and so on.
The Ballet Master may or may not also be the company's Artistic Director, who is the person actually directing the production(s) in question. Big companies would have them as different people.
A repetiteur is a person working under the Ballet Master who runs smaller rehearsals -- while the Ballet Master is working with the Snowflakes, for instance, repetiteurs might be running steps with 1) the mini mice, 2) party guests and 3) Arabian dancers, in three other studios. These would usually be other teachers, in a school environment.
The Artistic Director will only rarely also be the Production Manager (usually not, thankfully for their sanity), who is responsible for all of the administration behind the scenes - hiring department heads, booking rehearsal spaces and catering to feed the dancers, making sure there are water bottles and snacks backstage, paying the stagehands, etc etc.
Any one of the above may or may not also double-serve as the Technical Director, who is responsible for all of the physical bits - stagehands, lighting and sound cues and crew, building the set and props, etc.
The Stage Manager works directly with the AD, TD, and BM to set the cues and all of the ... everything for every show. Once a show opens, the directors generally bugger off and the Stage Manager is left to run all the technical things. The stage manager is present at every performance to 'call the show' - she'll be on a headset, giving orders to everyone from the orchestra conductor to the lighting board guys, telling everyone when to stop, start, go out, raise the curtain, move the lights, play this sound effect, run that light effect, etc etc.
You never step onto a stage without the permission of the stage manager. That's an easy way to get set pieces dropped on your head.
Crew has a whole stack of sub-disciplines as well (electrical, props, pyro, etc), of which any particular show may have one specialist for each, one for all, or none. The TD may also be running the lighting and sound boards; if so, he'll need at least one backstage assistant for everything else. I'd expect a crew for a show as big as Nutcracker to have at least 10 people, minimum.
The Head of Wardrobe is responsible for everything that goes on a dancer's body, which may or may not include props like glasses or masks, depending entirely on the relationships between the two departments and department heads. usually I'd say masks go to props and glasses and gloves to wardrobe, but that could go any way and be done somewhere!
The Wardrobe Master or Mistress is responsible for the day to day maintenance of the costumes, including laundry. They may or may not be the same person as the Head of Wardrobe -- either way, they're paid out of the dressing/run budget rather than the pre-production budget. For professional ballet companies, you've also then got your specialists: shoe person, tutu person, and often a hair/wig/hat/headdress person.
Dressers get the costumes on and off the dancers if required, during the show. Clara always needs a quick change, going from whatever day dress she's wearing for the opening scene to the nightdress she wears for the rest of the ballet. Sometimes the full outfit has to be changed, by a crew of people up to five strong, in under 20 seconds. (remember that note re: 'high stress'? Dancers also get touched, often by relative strangers, a whole lot.) You need at least five dressers to run a production of Nut.
... I went off on a total tangent. I'm sorry. XD