Although some use the term interchangeably they aren't the same thing - tracking is one element of the overall wheel alignment (essentially the whether the "toe" angles for both wheels match)
The issue of whether the steering wheel is "straight" or not is separate -but-related. It's possible to have the alignment 100% correct but the wheel position off-centre. Which is basically what happens when whoever is doing the alignment doesn't lock the steering wheel in a centered position while doing the alignment.
A good four-wheel alignment costs more than a simple "tracking" check - because it's more involved. All the possible alignment variables are checked (so toe, camber, castor etc).
FWIW I would say that 99/100 I'd be going for a proper alignment from a reputable shop. Especially when you consider that what most places will sell you as a "tracking" check is only done on the front wheels (as if the rears have no effect on handling!)