Do climate models model climate?

Climate models have been modelling global warming rather than the climate:

"In particular, green plants can be expected to grow as they find it
easier to harvest carbon from the air around them using energy from the
sun: thus introducing a negative feedback into the warming/carbon
process. Most current climate models don't account for this at all"

it appears that at current rates we have at least 200 years before there is any dangerous warming.

New NASA model: Doubled CO2 means just 1.64°C warming • The Register

A group of top NASA boffins says that current climate models predicting global warming are far too gloomy, and have failed to properly account for an important cooling factor which will come into play as CO2 levels rise.