Yeah, exactly. If the change happens as fast as it is happening, you get a mass extinction. If the change happens over thousands of years, biomes have time to migrate.
Using the xkcd timeline as a guide, the temperature change in the last 120 years is about the size of the temperature change between 11,000 and 9,000 BC, which was only mildly disruptive to global ecology.
The scale we're observing right now is the stuff of millions of years of change, or massive extinction events.