I think that they are different because they are used in different ways. For example, I'll use the sentence that you gave in the question: Your career is in jeopardy. This works, as well as in danger, but it doesn't work with hazard; 'your career is in hazard' is just not something that is correct idiomatically or is said at all. Also, the words 'hazard' and 'jeopardy' are not synonyms, as a fire hazard for instance is not a fire jeopardy. Yes, hazard and jeopardy are used in everyday life, and it is okay for you to say that your career is in jeopardy. But hazard, danger, and jeopardy are not 'almost total synonyms', so I think that before you research this more, you should see whether or not your 'a number of discussions on the internet' are reputable sources or not.