The reason for the talk of various generations of RAF history is a product of the reality of their particular situation during distinct time periods.

Essentially the Red Army Faction was "founded" in May of 1970 when famed journalist Ulrike Meinhof helped break convicted arsonist Andreas Baader from police custody in Berlin. The group, which consisted of as many as about 40-50 people in the coming two years, spent their time robbing banks, stealing cars, etc, until eventually beginning a bombing campaign in May of 1972 that left several American soldiers dead, and dozens of Americans and Germans maimed. Quickly the entire leadership was captured and imprisoned.

So with the leadership in prison, and only low-level followers still on the outside, new "blood" was needed to refresh the group. This came (partially) in the form of former members of the Heidelberg University "Socialist's Patients Collective" (these were literally mentally ill students of a professor who believed that their mental illnesses were the product of Capitalism, and the cure for their illnesses was to attack the state). They formed the core of the so-called "Second Generation of the Red Army Faction." They were called this in the popular mind to differentiate them from the original leadership, and to emphasize that most of these members joined after the first generation had been imprisoned.

So it really was a distinct group of folks.

The so-called "third generation" is much more nebulous; this is the group that generally led actions after 1977, after the major leaders of the group committed suicide in prison (Baader, Meinhof (in 76), Gudrun Ennslin, and Jan-Carl Raspe), and much of the second generation were also imprisoned.

Truth be told, many people in the "second generation" could be considered "third generation" members. Such as Brigitte Mohnhaupt; who was clearly the prime leader of the group after 1977, yet she was clearly a member of the second generation as well.

One reason that the you will hear of a "second" and a "third" generation is to differentiate between the goals of the two generations. The second generation was essentially consumed with securing the freedom of the imprisoned first generation leaders. Their actions, such as the failed 1975 German embassy takeover in Stockholm, or the 1977 kidnapping of industrialists Hanns-Martin Schleyer, or the 1977 hijacking of a Lufthansa plane in Palma Mallorca... all of these were done to secure the release of Baader, Ennslin, et al. Once they died in prison, the "third generation" basically turned their focus on attacking the state; they no longer were consumed with getting leaders out of prison.

It's important to note that many supporters or followers of the group do exactly as you suggest; they consider it on long, unbroken history. In reality that is just as valid of a way of looking at it; the talk of the "Generations" is merely a way to understand why their actions changed so dramatically during distinct periods of time.

Source: my site: baader-meinhof.com