The first garage are offering 4 wheel alignment that checks a whole heap of angles to determine the centre line of the car, castor, toe, camber etc etc. It will show up any adjustments that need doing, or damage from impacts etc resulting in bent components.
The second garage are offering basic tracking, which basically means are the front wheels pointing in the right direction and not scrubbing, you could be missing a rear wheel and it wouldn’t notice 🙂
I’d always go for the more expensive alignment after experiencing the transformation it made to our Mondeo, both in handling and excessive tyre wear.
Edit: My car was an unruly monster and turned into a poised cat after being tweaked. I had it done shortly after buying it, and a couple of years later when we sold it I could tell it was going bad again. It was the rear toe that was going out of adjustment.