Essentially, living in Australia on a student visa places some restrictions on a student visa holder in two main areas, being education and employment. In terms of education, an example of such restrictions is the inability to study a degree part-time which may be applicable at different institutions, USyd being one (there may be exceptions, although that is generally not the case). On the other hand, Australian citizens and permanent residents can study part-time or full-time.
In terms of employment, there are restrictions imposed by the government, such as the maximum number of hours of work that a student visa holder is allowed to work. This is 48 hours of work per fortnight in most cases, except where otherwise specified. Another restriction is placed by some employers, which is that applicants must have full working rights to be eligible to apply for a role, i.e. they must be Australian citizens or permanent residents. When this is the case, you may find information in a job description similar to this:
"To be eligible to apply for this job, you must be an Australian or New Zealand citizen or have an appropriate visa to be able to live and work in Australia."
If you cannot find this information, you may be eligible to apply. In fact, I accessed the application form for a Chemistry Cadetship role at BlueScope Steel, and one of the options in response to the question about your right to work in Australia is
"I hold a current visa that allows me limited working rights in Australia". This means that they may consider applicants who hold a student visa. Of course, it still would not hurt to contact BlueScope Steel directly to confirm this.
I hope this helps!
