Patrick,
There is much difference between the two.
You appear to work in the vicinity of an emergency room. You have a better awareness than many of the stunning rapidity with which things can go wrong.
Diving is not necessarily more dangerous than flying an aircraft. Like piloting an aircraft, however, diving is intolerant of error or oversight. It is deceptively easy to get into a situation that is difficult to get out of.
I encourage you to consider taking the week-long course (at least) like Rick's, which provides the complete training program over a period of time that allows for an in-depth understanding of the fundamentals of safe diving.
I agree with Johnnythan. It is not merely a matter of the number of hours. It is the number of classroom hours combined with time spent reading the book and absorbing the material. There are several concepts that are important to grasp for a good, safe foundation.
I agree also with Peter, that comfort level in the water is also important, and will only be gained by time spent in the water. Having a good theoretical foundation, though, allows you to better integrate the experience you gain in the water with the rationale behind WHY you do the skills you practice.
Peter may be correct with his statement that many divers go through very cursory certification courses and do not have 'problems'.
This could be because the crash training was adequate. Another explanation, however, is that those students have not yet had enough experience diving to encounter a situation which requires more training than they have received.
Those divers who DO have 'problems' often have them because they are diving beyond their own capabilities and experience/training. Having an in-depth foundation is important.
All things considered, you will be a better-informed, safer diver by investing quality time as well as dollars in your own training.
Regards,
Doc