What are the differences in responsibilities among them? Can anybody give me an example to elucidate that. Also why are non-tenured faculty more interested in a co-adviser role than a committee member role?
The advisor is the person who is formally recognized as the person most responsible for supervising the student's thesis research. A co-advisor is a person who also works with the doctoral candidate, but often in a secondary role (perhaps providing scientific but not financial support, for instance).
In my own case, for instance, I had two advisors who were fully equal in both supervising the research and supporting it financially. However, formally one of them had to be in charge of the thesis research—I believe they decided it by a coin flip.
The thesis committee is a body that convenes only sporadically (although sometimes on a regular schedule) to ensure that a doctoral candidate is progressing according to expectations. The committee—which usually includes the advisor and several other faculty members (or other advisors)—is also usually responsible for deciding when a candidate is ready to schedule a defense of the thesis and graduate.
As you can see, this is a very different role than a co-advisor, who takes on a much more active role in supervising and guiding the doctoral candidate's work. While a thesis committee member rarely is a co-author on a paper with the candidate, a co-advisor often will be. Consequently, it's much more useful for a faculty member to be a co-advisor than simply a committee member. (The latter role will not carry anywhere near as much "credit" toward a tenure case as being an advisor or a co-advisor.)
This breakdown of the different roles comes from the University of Melbourne:
In committee meetings (12 month confirmation, 2 year review, etc.) the chair organises the paperwork, basically. They are also there if the candidate needs to confide about their supervisors and potentially make a complaint if one of the supervisors' actions is unethical, or if there is some kind of professional or personal issue between them and the candidate.
As to your second question, I would suggest that non-tenured staff/faculty would push to be a co-adviser rather than committee member, because it raises their supervisory profile whereas being a committee member is really just a bureaucratic position. When applying for tenure-track positions, employers will look at the theses that the person has supervised or co-supervised, in addition to a range of other things, obviously.