MAP measures pressure. MAF measures air flow. Both can be used to determine fueling. As OVERKILL said, just using a MAP sensor is typically called Speed Density, it uses the reading from the MAP sensor (as well as usually an air temp sensor and coolant temp sensor) and then calculates fuel needed from a table in the ECM. MAF tends to be the more accurate system and is what is used in pretty much all modern vehicles, as it is also more capable of variation.
But back in the late 80s/early 90s, MAF sensors were not anywhere near as accurate as they are today. In fact, many were very inaccurate, as in the case of the Bosch MAF used in my 89 Camaro. I ended up doing an ECM conversion and going to the 90-92 version that uses Speed Density so the car would run better and be easier to tune. Today MAP is mostly there as a backup in case the MAF fails. If that happens, the PCM will move over to the backup Speed Density mode, turn on the SES light, and at least keep going until you can get the MAF fixed. A lot better than the terrible limp mode of the older computer controlled cars that pretty much did nothing.