This topic comes up now and then and I thought it might be handy to have some reference material. This first post is the glossary entries under "Climate Sensitivity"
Climate sensitivity The change in the surface temperature
in response to a change in the atmospheric carbon dioxide (CO2)
concentration or other radiative forcing. See also Climate feedback
parameter.
Earth system sensitivity
The equilibrium surface temperature response of the coupled
atmosphere–ocean–cryosphere–vegetation–carbon cycle system to
a doubling of the atmospheric carbon dioxide (CO2) concentration
is referred to as Earth system sensitivity. Because it allows ice sheets
to adjust to the external perturbation, it may differ substantially from
the equilibrium climate sensitivity derived from coupled atmosphere–
ocean models.
Effective equilibrium climate sensitivity
An estimate of the surface temperature response to a doubling of
the atmospheric carbon dioxide (CO2) concentration that is evaluated
from model output or observations for evolving non-equilibrium
conditions. It is a measure of the strengths of the climate feedbacks at
a particular time and may vary with forcing history and climate state,
and therefore may differ from equilibrium climate sensitivity.
Equilibrium climate sensitivity (ECS)
The equilibrium (steady state) change in the surface temperature
following a doubling of the atmospheric carbon dioxide (CO2)
concentration from pre-industrial conditions.
Transient climate response (TCR)
The surface temperature response for the hypothetical scenario
in which atmospheric carbon dioxide (CO2) increases at 1% yr–1
from pre-industrial to the time of a doubling of atmospheric CO2
concentration (year 70).
Transient climate response to cumulative CO2 emissions (TCRE)
The transient surface temperature change per unit cumulative carbon
dioxide (CO2) emissions, usually 1000 GtC. TCRE combines both
information on the airborne fraction of cumulative CO2 emissions
(the fraction of the total CO2 emitted that remains in the atmosphere,
which is determined by carbon cycle processes) and on the transient
climate response (TCR).
"The Earth’s Energy Budget, Climate Feedbacks and Climate Sensitivity", Chapter 7 of "The Physical Science Basis" in the IPCC's Assessment Report 6 is the place to cover this topic. If you don't already have one, you can download a copy of the entire document at:
AR6 Climate Change 2021: The Physical Science Basis — IPCC
Chapter 7 begins on page 923.
Climate Feedbacks are discussed in section 7.4, beginning on page 967.
Estimate of ECS and TCR are discussed in section 7.5, beginning on page 992