Thank you for the replies.
Alexander: Thanks I just did not figure out that the difference was the equilibrium. The articles I found were not consistent, however it should have been clear.
That is the point that a little Googling led me to, Dr. Szwarc's metaphor for this particular type of chain reaction polymerization is a useful one, and has entered the jargon since the '50's. But 'quasi' hasn't, and there have been calls for some sort of standardization of terms.
The link I found is quite interesting, it must have been written years ago, when the hypertext nature of the web was new, they actually try to make the links, to the links, to the links of the terms. We tend to not do that anymore. It is known that, whatever the topic, once you go a few links in, you usually connect to porn sites.
Fortunately, that page only links to itself, which is safe. But there are lots of different ways to describe chain reactions of polymerization. And this 'living' term isn't a great choice -- as a molecular biologist, 'living' and 'polymer' mean proteins and nucleic acids, for example. Furthermore, nowadays, self assembling carbon fullerene tubes are all the rage. Once we start combining self assembling microtubes, bio-engineered macromolecules, with the usual non-biological polymers in research procedures and even in manufactured products, this is all going to get muddy.