How Advisors Are Not Like Bosses

In a number of very critical ways, being a grad student is not the same as having a job. One of these is the difference between your advisor and your boss.

Academia is a weird place sometimes, and part of that is due to the organizational structure. Superficially, it's not a terribly odd organizational chart, but many times, the actual nature of the relationships in academia is fundamentally different than the analogous relationship in industry.

Difference #1: Deadlines
Graduate school is sometimes a strange limbo of hazy requirements with no firm timeline. Other times, there are firm deadlines, but these are somewhat sporadic. Your advisor is not going to stop by your desk and say "I need the report for the widget on Tuesday for the division meeting." (most of the time).

Difference #2: Performance Reviews
In graduate school, it is unlikely that you will ever sit down for a formal performance review with your advisor until it's approaching time for your defense or unless your professor spent time in industry. More importantly (from the grad student side), you will also never review your advisor's performance. Some larger corporations have a system from underlings to review their managers. Grad students don't have this sort of mechanism, so we resort to whining on the internet.

Difference #3: Advice 
Advisors, at least in theory, are there to help give you advice about how to advance your career and achieve your goals. While there are managers who do this, it's not strictly speaking part of their job. Of course, there are also advisors who aren't very good at this, but it's in the title...

Difference #4: Dependancy
If your manager quits, gets fired, or moves to a new position, this means you get a new manager, but may very well still be working on similar projects, and things are relatively stable (assuming everything goes smoothly). Having an advisor quit, move, or get fired can be much more difficult. You're typically required to have someone advising your research, and if you're very far into your project, switching advisors could very well entail losing years of work. If your advisor is moving, you might be able to follow them, but that's not an easy proposition in most cases.

You also very likely depend directly on your advisor for funding and access to resources. There's not someone above them you can go to (i.e., your boss's boss) when you need order forms signed and they're out of town. The independence of your position is much murkier: you don't work for Corporation or University, you work for Advisor at University. Different schools may also deal with this differently, adding to the confusion.
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I'm sure there are plenty more differences, and that there are special cases that disagree with every point I've made above, but in my humble experience and observation, these generally have been true.