It also indicates how long they've been in service, because they would have made their aprons when they started working, and followed the fashions of that time. Look at Anna, who's head housemaid. Her apron is older, and therefore more old-fashioned (it looks like something from the very turn of the century rather than 1912), because she's been working there longer, so she made her apron earlier than Gwen made hers. The design of Gwen's apron only looks a few years old.
O'Brien doesn't wear an apron because she's a lady's maid, and lady's maids didn't do any kind of work that required an apron to keep clean. They dressed the lady they worked for, did her hair, altered and mended her clothing, and sometimes made simple pieces (especially underwear, for some reason).
Mrs. Hughes doesn't wear an apron because she's the housekeeper, which is a management role. So she's not scrubbing pots or dusting the sitting room. Housekeepers directed the housemaids, consulted with the lady of the house about events (guests, dinners, etc.), hired and fired female staff, and kept household accounts. She might have donned an apron to make jams, cordials, and herbal medicines (for the staff) a few times a year , but she didn't wear one as part of her day-to-day wardrobe.
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