From my understanding, the transfer from 2wd to 4wd is a hydro mechanical process. But, if you have the 3.5L engine, then it is an electric process. I talked to a buddy that had an 02 Santa Fe with the 2.7L and he said he had an issue with the hydraulic system. He didn't explain any more about his issue.
I wanted to make a comment on this and forgot to before.
2003 is the first year Santa Fe's had the fulltime 4WD option. That is indeed an electrical system. As I put in my previous post, the fulltime 4WD is always on. It doesn't come and go. And the reason it's able to do that is that a computer will shift power around on it as needed.
That 2002 Santa Fe with a 2.7l is AWD and is hydraulic. It's a complete different system that comes and goes as needed. So any issue that was happening with this vehicle would have absolutely nothing to do with any problem a 2003+ fulltime 4WD might have.
Traditional 4WD has to be turned on because you generally don't want to drive on dry, non-slippery surfaces. It can cause stress on the parts which is why even in 4-high gear you can't go over a certain speed usually.
The Hyundai fulltime 4WD gets away with it always being on by having the computer adjust the slippage so it doesn't cause the stress that having a traditional 4WD on all the time would cause. The Mercede's M Class SUV's also had a similar fulltime 4WD system, but they had the additional option of a 4-low gear like traditional 4WDs have. I really wish the Santa Fe had a 4-low option.