No, not all scanners are the same. They range from code readers (like what your part store has), to full blown scanners that list tons of information on your vehicle (like the current rpm, how much fuel it's using at that exact moment, historical graphs and data, what all the sensors data is, etc.) The more complex the machine, the more expensive it is. Then there are the scanners that only the dealers can get/afford, which have security information and computer programming information.
All the codes are standardized. On the more advanced scanners, the code is displayed on the screen, with the description. Then the mechanic checks the sensors that the code is referring to to see if it's a malfunction of the sensor or a malfunction of something else. If the sensor is reading some information, then the problem is somewhere else. If the sensor looks "dead" then the sensor needs replaced. For example, if the code is for an oxygen sensor, then we can check the data coming out of that oxygen sensor. By reading this data, we can determine if the sensor is malfunctioning or the catalytic converter is bad.
No, we can't just shut off the light without finding the reason it was on if there is truely a problem with the vehicle. The light will come right back on again after two trips, if there is a bad part.
Source: work in an auto repair shop.