100% Renewables by 2050 will Save Money, page-14

You are right in your definition of climate but the popular media has defined climate change as:

"a change in global or regional climate patterns, in particular a change apparent from the mid to late 20th century onwards and attributed largely to the increased levels of atmospheric carbon dioxide produced by the use of fossil fuels"

This confusing but common definition is better stated as AGW.
The validity of
- measurable changes in climate
- a 20th century warming trend
- the contribution to the above by man specifically increased CO2
are 3 separate questions and are best handled as such.