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.

https://en.wikipedia.org/wiki/Phonetics says: Phonetics (pronounced /fəˈnɛtɪks/) is the branch of linguistics that studies the sounds of human speech, or—in the case of sign languages—the equivalent aspects of sign.[1] It is concerned with the physical properties of speech sounds or signs (phones): their physiological production, acoustic properties, auditory perception, and neurophysiological status. Phonology, on the other hand, is concerned with the abstract, grammatical characterization of systems of sounds or signs. From that I guess you can infer the difference, although you probably should be aware that if "phonologist" and "phonetician" really exist as words, they are very specialised, if not jargon terms. I have never heard or read either of them before.