From "kusina" come the words "kusinero" (male cook) and "kusinera" (female cook). These words are from the Spanish "cocina", "cocinero", and "cosinera". In Spanish, a chef is also a "cocinero/a", but in the Philippines, a chef might feel insulted if you'd call them "kusinero/a". So, they have to be called "chefs".
Here's why. In the olden days, beginning with when were under Spain, a "kusinero/a" in a Philippine household has the same rank as a servant, except that the work is dedicated to the kitchen. Eventually, but before culinary schools were established here and produced chefs, cooks in restaurants were also called "kusineros" with practically the same stature as any of the staff. Maybe they get paid a bit more, but that doesn't really put them in a class above the rest.
Up to now, if you're talking to ordinary people whom you don't think have helpers/servants at home and you'd like to find out who cooks for them, you have to ask it this way: "Sino ang nagluluto sa inyo?" (Who cooks for you?) and not "Sino ang kusinero/a ninyo?" (Who is your cook?). That's because if it is, for example, the wife or the mother who does it, then the second question would come across as degrading to those concerned. If you're quite close to the person you're asking, then the question may be regarded as you trying to be humorous, otherwise, never ask it that way.
You may use "kusinero/a" for the cooks up to the level of ordinary restaurants, but above that, "chef" or "cook" would be the safer choice. For those who cook at home, use the verb "nagluluto" (cooks/cooking) instead, or if you have a tendency to flatter, use "chef".
Also, if you're here, you may come across the term "dirty kitchen". I don't think that it's a term used in many countries. Here, it means a rudimentary kitchen that's constructed apart from, but adjacent to the main house. Those who have the luxury of space and an extra budget might have a dirty kitchen in addition to their regular kitchen. That's where they do all the messy work involved in cooking. It also helps in preventing the smell of some dishes from getting into the main house. The term is always said in English though. That's because it translates to "maruming kusina/kusinang marumi" in Filipino and saying it that way would be understood to mean that it should be cleaned.
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