Yes, participating in a job interview is a type of public speaking. Yet, no one tells you that you are likely to feel as terrified as if you were delivering a formal speech. So, you assume you are so nervous for the wrong reasons, e.g. not being the best candidate. Also, few agree with you that the situation is high stakes.
You are right to approach the job interview with the same seriousness, willingness to practice and to solicit feedback from others as do keynote speakers. Here are four tips:
Research. The more you know about the organization and the interviewer the more you can anticipate the questions asked, the curve balls thrown and the hostile comments. Regarding the latter, had a lawyer asked around about the small law firm she interviewed at she wouldn't have been thrown - and unable to respond - to a series of mean remarks. The firm is known for its lack of social skills. Since jobs are scarce in the downsizing legal sector, this person wanted the job. Her regret was that she wasn't able to neutralize accusations that she had had too many jobs in her career. She could have explained how much more she had learned from the diverse settings than she would have in any single job.
Tell the story they want to hear. Interviewers usually have a set idea about the professional they will hire. The trick is to figure out that composite and then present yourself as it. You are not there to present yourself. You are there to align with what they have in mind.
How do find out what their ideal candidate is? Read between the lines on the help wanted. For example, it will be obvious that they want you to work all the time. Let them know in the interview you are all-work, whenever. Also, ask around about the organization's culture. It may be conservative. You present yourself as totally buttoned-down. Read third-party reports on the organization.
Hold the personality. The era of personality is over. Organizations need a warm body to do X task. End of story. Yes, present yourself as friendly and enthusiastic. But leave it at that. There are exceptions, of course. One would be if you are applying for a sales position.
Mirror. The fundamental of selling anything, including yourself for a job, is to simulate the ethos of the organization and the interviewer. If it's Millennial cool, you will present yourself in a casual manner. If the interviewer speaks fast you will pick up speed in your normal pace.
A lot of this you can find out by research before the interview. Once there, do a quick scan of the waiting room, the interview room and the person conducting the interview. Then adjust everything from tone of voice to body language to click in the pieces.
As with delivering speeches, the more interviews you do the more skilled you will become. That's why it's useful to apply for just about anything in order to access interviewing experience. If you continually strike out, you could ask the interviewer for candid feedback on what you could have done better. I did that with the executive director of a non-profit in central Connecticut. She took me out to lunch and brought along the first client for my business. Caringly but firmly she told me I should be an entrepreneur, not an employee.