Different institutions have different policies with regards to tenure track and non-tenure track. It also depends on what department you are in and the capacity of your work. Tenure and non-tenure was explained to me as such:
If you are a basic science researcher, tenure is very important. All tenure means is that if you were to cease academic activity, you are guaranteed a base pay (i.e., let's say you run out of grant funding). However, the base pay is quite low. In the sphere of laboratory investigation, tenure is often equated with "job security." This can be misleading because if you, as a researcher, cease all activity...sure you can keep your base pay. But job security means very little when your department dislikes you for your lack of activity and wants to get rid of you. The department can actually do some passive aggressive things to make your life more miserable so that you will want to leave and give up your base pay. Think of what happens to Milton in the movie, Office Space. Lumberg never actually tells him, "you're fired", instead he just tells him to keep moving his desk and eventually into the basement. As a lab investigator who no longer has funding, his/her lab space is taken away and given to someone with funding and he/she is relegated to a small, closet-spaced office. Would you stay for base pay? Or would you leave and look for different but greener pastures?
As a clinician, tenure is not as important. You provide an essential service to the hospital; hence, you simply just lose your job if you don't do anymore clinical work or you suck so badly at it. Plus, in many departments, you don't have to publish to keep your job. It's just that if you don't publish, you don't get promoted. Teaching won't get you promoted; however, teaching at a national or international stage will help you. To be recognized enough to be invited to do the latter, you have to publish. So for promotion, there's no way around publishing. Pure and simple. Again, if you provide an essential service to the hospital, you won't lose your job. Hence, in that vein, the concept of tenure is practically trivial for the clinician. Tenure and promotion is more a matter of personal pride. Some people choose not to care about either. That is why you can have a person who loves to teach, refuses to publish, and just retires as a Clinical Assistant Professor Emeritus with a good retirement package.
Someone mentioned Duke and Hopkins. Those two have quite a difference in track setup. Duke has three tracks...and the clinical track exists. However, you start on this track without tenure. If you are recruited from the outside, you should start as an Assistant Professor. Next step is Associate Professor. Next step is Associate Professor WITH tenure. Final step is Professor (you're already tenured). NOTE: There are 4 steps. You might as well call the Assistant Professor an Instructor and the Associate Professor without tenure as an Assistant Professor. So what? Who cares? There's nothing wrong with that. As long as you keep your job, right?
Hopkins has only one track. It's a tenure track. But when you start, the clock starts ticking; it's essentially publish or perish if you break it down to the bare-bones essentials. You can consider your job in jeopardy if you don't publish (not sure what the quota is though). But the people they recruit are quite good so for the most of them, this may not be a problem.