I can tell you all about SAR if you'd like

but, long story short to answer your question- SAR dogs do both air scenting and trailing- which in reality, is a distinction that only humans make. Most (if not all) dogs that are scenting for something will go back and forth interchangeably.
SAR is a huge investment, both financially and with time. I don't think anyone has mentioned the thousands of dollars you will have to spend on wilderness gear. The gear isn't something you can go 'half way' on either- cheap boots feel like cheap boots after 10 hours, and in the backcountry, thats the LAST thing you want. You need a rescue pack, all the gear to survive 24hrs in it and then some. Then theres the clothes and stuff like that. I've spent so much money on gear that if I looked at all the receipts, I'd probably feint! and thats with me shopping sales/online/etc. Not including gas or anything!
The time requirement is also really extensive- Our practices are twice a week at 2-6 hours each. (mine has an added drive time of an hour- boo!) Not including time they expect you to be working on home training with the dog (15-20hrs/week). Also they hold week-long SAREX (search and rescue exersizes) that are mandatory, or you'd better have a darn good excuse! Then there are missions themselves- no only are we dispatched anytime, any day, but the searches are often held over days, possibly weeks. The last live search I was on went for 8 days, we drove out there and stayed the whole time.. searching 14hrs+/day.
Its not really a hobby type thing, I would say. All that said, if you have any really specific questions about SAR or scenting theory, feel free to PM me. While Callie will be my first SAR canine, I have years of experience as a ground team search and rescue member.