Phonetics and phonology are related fields (and I have personal interest in them). Phonetics is the study of individual speech sounds. Phonology is the study of the speech sound system of a language.
What is the context for these terms? Speech pathologists are trained in phonetics and phonology. Some teachers (not many) are trained in phonetics and phonology. Linguistics researchers at universities might have been called phoneticians (researcher specializing in phonetics) or phonologists (research specializing in phonology) once upon a time. I am relatively sure that I have read old linguistics textbooks that referred to phoneticians in the 1880s who suggested a special alphabet to represent sounds (precursor to the current International Phonetic Alphabet (IPA)). However, I don't remember seeing the terms phonetician or phonologist in recent memory.