I think 漁民 and 漁夫 is very similar. even I can tall you that there is no difference.
and yes, 漁民 and 漁夫 means who do it professionally. is a job, and also a kind identity. like 醫生 (docter)、老師 (teacher).
and 捕魚者, actually. we seldom use this word.It is just the other way of saying a word for 漁民 and 漁夫.
I can give you more explaination.
捕 is verb. is an action. means catch.
魚 is noun. means fish.
者 is noun. means the person who does the thing. Like the "er" in worker in English.