In the world of cabinet manufacturers, I've found that the difference between the terms stock, semi-custom, and custom is not as clear-cut as you might think. Semi-custom, in particular, has always seemed ambiguous to me.
Stock cabinets are pretty straightforward. They're manufactured in standard sizes and supplied through distributors to places like The Home Depot, local lumberyards, and specialty kitchen and bath shops. Their carcases are typically of particleboard, though their doors, face frames (if they have them), and drawer fronts are usually of hardwood. Manufacturers keep the cost of their stock cabinets down by using simplified drawer construction and thinner paper-laminated particle-board in areas of the cabinet that are not readily visible.
Semi-custom and custom cabinets often have the same hardwood drawer fronts, doors, and face frames as their less expensive stock cousins, but their carcases and drawers are usually of a higher-quality construction. While a stock-cabinet drawer may have particleboard sides stapled directly to the drawer front, better cabinets will have four-sided drawer boxes, often delivered, of solid hardwood screwed to the drawer front. Also, better cabinets will have sturdier carcases built of veneered plywood rather than particleboard (although MDF with either a melamine or high-pressure laminate surface is often used in high-quality face-frame and frameless cabinets).
Both semi-custom and custom cabinets are made to a specific customer order, rather than premanufactured, and require a sometimes-substantial lead time of between 3 and 12 weeks for delivery. For the close to 25% more that you can expect to pay for custom vs. semi-custom cabinets, you'll see minor upgrades: 5/8-in. vs. 1/2-in. drawer stock, for example, or extended stiles rather than wood filler strips. In some cases, custom cabinets can actually be made slowly larger than standard size, though this varies from manufacturer to manufacturer.
Will one grade hold up better than another in the sometimes-hostile bathroom environment? The major functional difference between the three types of cabinets is in the type of drawer that they have. If Kitchen Cabinet Manufacturers Association (KCMA) certified, it's definitely that installed custom-cabinet carcases will last any longer than KCMA-certified stock carcases, and in most cases the door frames and drawer fronts will be virtually identical. But the drawers are where the differences will show up over time.
For all three types of cabinets, you're limited to styles and sizes listed by the manufacturer, although in some cases custom cabinets can be ordered with an oversize stile to fill in a gap (rather than having to rely on a screwed-on filler strip) or even in a slightly larger size. Other differences are usually minor and depend upon the manufacturer.