As you’ve noticed, “shot breakdown” is used in a couple of different ways in the industry. If an employer is asking for a breakdown with your demo reel, then it is as Leigh describes: a list of the shots on your reel and what work you did on them. Since CG is a collaborative effort, both in the real world and in school projects, you may not have done 100% of the work on every shot on your reel, and the shot breakdown just states what you did per shot (and usually a list of where the material came from (i.e. school project, such-and-such film, such-and-such commercial, etc.), and the running time as well as what the artist contributed.
When you are talking about a “shot breakdown” from a CG or VFX Sup point of view, then it is as Sundialsvc4 mentions where you take a shot and determine what props and environments show up in the shot, what characters are present, where crowds or fx are used, what scenes you are doing cloth or hair sims for, what is going to be a matte painting and what will be modeled, etc. On effects shows, the shot breakdown will be used to determine what will be CG, what will be practical, etc. These breakdowns are used for budgeting as well as determining who gets assigned to what work.
From the productions I’ve seen, decisions as to whether a static background element is rendered once and re-used or rendered for every frame is generally left to the lighter of the shot to decide themselves, as even objects that don’t move might have animated light effects on them. Also the lighter (or more likely the Lead Lighter) will determine how they want to break up the render passes for the sequence, with shot lighters further tweaking it to their own needs.
Same term, different meanings depending on context.