(1) What is a "statement of teaching interest?" How does it differ from a "teaching philosophy" or a "teaching statement"?
I would guess that all three quoted phrases mean the same thing. The "teaching statement" is not as formalized a genre as the sonnet: there is a range of reasonable responses, and to my ear all three things are asking for the same range.
Of course, if one is especially interested in a specific teaching position it would be better not to guess but to inquire what they mean. I don't see any reason to be shy about that: just ask politely.
(2) How does one write this statement without any classroom teaching experience?
Others have given some advice on this. It is certainly possible to literally write a teaching statement without any teaching experience -- one talks about one's teaching philosophy, teaching goals, and so forth, while not mentioning the experiences that one hasn't had. It's not like they're asking for the secret masonic handshake: anyone who has gotten a PhD has certainly experienced enough teaching to be able to write about it intelligibly (let me assume that someone who has gotten a PhD has learned to write intelligibly on academic matters!).
However, isn't there another key question here? Namely:
(3) What are the chances that someone who has absolutely no teaching or TAing experience whatsoever will be seriously considered for a faculty position with emphasis on teaching?
I can answer this question from the perspective of a math department at a research university: it is very likely that I would not seriously consider any such candidate. Let me explain. "Even" at a research university, teaching is a big part of the job -- roughly half, according to university directives -- and someone who is a truly unsatisfactory teacher is going to be an eternal liability and problem. Well, you say, what if they are a truly outstanding researcher -- can't they learn to teach? It doesn't really work for me. If by "truly outstanding researcher" you mean that they've proven the Weil Conjectures, then they deserve to be at a truly top place which can afford to have faculty who literally never teach, or who only teach graduate seminars to their own brilliant students. Any candidate like that is not going to come to my public research university, and if anything still less is she going to go to a teaching college. If someone is simply a strong enough researcher that I would otherwise be very pleased to hire her, then her complete lack of teaching experience creates an insurmountable fairness issue when one compares her to other candidates with similar or moderately worse research profiles but who have devoted a substantial amount of time and energy over the years to teaching. Even serious research mathematicians work hard to be competent teachers: it takes time and energy. Sometimes people have less than stellar teaching, and it really can ding them a bit even at a "serious research university". Someone with no teaching has to get a zero averaged in to her total grade, so to speak.
I explained how it goes for mathematics at a research university. The OP's candidate is changed twice: from mathematics to biochemistry, and from a research university to a teaching college. From what I've heard on this site, teaching experience is valued significantly less in the non-mathematical sciences than in mathematics. On the other hand, I happen to know that teaching experience and credentials are valued way more highly in teaching colleges than at research universities: though I think of myself as a "serious teaching guy", when I visit a colleague at such a place I feel like I am hiding in a foxhole doing math all day compared to them. Moreover smaller places are smaller, so the "ethos of the college" is something which is more strongly felt by all, whereas being a scientist at a research university is almost a different job from being a humanities professor at a research university. My best guess: there is little chance that someone without any teaching experience will get any real consideration at a reputable teaching college.
So I would say to the OP: if your friend wants this job, it's not about how to write the teaching statement, it's about how she can acquire some actual teaching experience. One semester of good evaluations in any reputable post high school academic institution would make a world of difference. If she's not willing to acquire that, is she really that serious about a teaching career? Compared to the other candidates, I mean?
Two final points:
I. I do not want to leave the impression that one should write a "teaching statement" that hides the fact that someone has no teaching experience. Although this should come out elsewhere in the application -- e.g. on the CV -- in my view it would be dishonest not to at least remark on this in the statement itself.
II. Others have counseled that a teaching statement should "[l]ook at what the professionals say about teaching" and "use pedagogy literature". This is good advice, but it can be misapplied. Namely, you need to have real understanding and ideally mastery of anything you talk about in these job applications. Most people know not to talk about locally ringed topoi in their research statements if they do not want to get asked what a locally ringed topos is in an interview. However, at least in my line of work, it is something of a cliche that young people "use pedagogy literature" to the extent of absorbing some trendy buzzwords, which they then misuse. If you talk about flipped classrooms, IBL and so forth and reveal that you don't fully understand what these terms mean, that is so much worse than not using them at all.
In fact at my research university (it is a bit different at teaching colleges, I happen to know) most of the faculty are not familiar with the pedagogy literature, and if I'm honest, some people pride themselves on the conjunction of that ignorance and their superior teaching. I don't think pedagogical literature is BS (or not all BS, anyway; every branch of academic literature has some BS), and I do believe that if you actually learn these ideas and articulate them properly and well it will be to your credit. But be careful. Also be aware that the trendy technique that one committee member might like might make another one roll her eyes. So a good teaching statement succeeds independently of its use of this kind of terminology and ideas.