Is there a difference between faculty position at a State university and between public university in terms of employment conditions, salaries, research funding and politics (e.g. faculty position at Alabama State University versus University of Alabama; Arizona State University versus University of Arizona)?. All universities that I am interested in are research universities. Thanks.
State universities are public universities. The other main type of university would be private, non-profit (I'm assuming you are not looking at for-profit universities?). Public universities are often controlled by the state legislature, so they are sometimes vulnerable to political decisions, such as cuts in funding, determination if faculty get salaries, the number of courses required to teach, etc. For instance, during the recession, California had a budget crisis and there were constant talks of faculty lay-offs at state universities. The amount of salary offered to faculty vary based on your discipline and the university. Some private universities may offer higher salaries, some may not. You should look at the individual school. In many states, faculty salaries at public institutions are public record and you can see how much faculty earn, if that helps with your decision.
Since state governments control state universities, the university norms differ from state to state. I previously was at a state university in Florida and now I'm at a state university in Alabama. The University of Alabama has a lower research designation than my previous institution (I was at an R1), but there are fewer universities in Alabama and UA is the state's flagship school, so I am provided with a better salary and more support for my research than I was before. Also consider the cost of living where individual universities are located, versus salary. The cost of living in Alabama is much lower than where my previous institution was, in Miami.
The take away? Find the faculty positions that are related to your work and compare institutions then. Hope this helps. Good luck!