厨师 is the formal/professional term. In casual speech, 大厨 ('big cook') is used as a compliment, similar to 'master chef.' 厨子 is more colloquial and sometimes slightly less respectful.
culture
Chinese cuisine distinguishes between specializations: 面点师 (pastry chef), 烧烤师 (grill chef). The head chef is called 主厨 or 行政总厨 (executive chef).
