So SW argues that language is inherently intertwined with human cognition, rather like how the parts of the brain are all interconnected and working together as we think. Strong SWism is pretty thoroughly debunked, weak is tentatively accepted on a spectrum.
I think that they might be trying to refer to generative theory versus cognitive theory. Again, it's been a while, so I might be wrong, but:
- Generative theory is Chomsky et al. who believe that there is a single inherent underlying pattern to language that restricts it, and that one could, in theory, figure out all possible syntaxes, for example. Similar to how phonology and phonetics are obviously constrained by our biological makeup (we can only make certain sounds), the argument is that other structures are as well. Basically that although they all seem different to us, languages are more alike than they are different because they come from a single source. Also Chomsky and co. consider this approach cognitive; the linguists are just infighting.
- Cognitive Linguists believe that language, and the systems that produce it, are under evolutionary pressure and that they change and shift in response to the environment.
Basically, if you took 10k people and dumped 5k of them on one planet and 5k on a planet that was the physical opposite, forbid them to contact anyone, and visited 2000 years later, Generativists say you could find a system in common between the two and cognitive linguists say you probably couldn't, because the systems themselves would have evolved to have different starting points.
Chomsky + GG: Person is born, person hears speech, person reaches for inherent language patterns in brain and uses them to understand/learn.
Cognitive: Person is born, person hears speech, person picks up on the system from the speech and is encouraged to do so/pattern match by social reinforcement.
No linguist that I'm aware of would claim that language is just an I/O system.