Mitigation
To explain it in a cliché, "prevention is better than cure". Mitigation actions ensures that actions taken can reduce the change in climate. Examples of actions include improving energy efficiency, conserving forest reserves or reducing the use of fossil fuel based energy.
So, what are there besides mitigation?
Developed countries had been focusing on making the Paris Agreement more mitigation-centric (kinda ignoring communities that have been affected by climate change). Developing countries, on the other hand, wanted a more diverse agreement that addresses all issues.
Adaptation
Adaptation refers to actions that countries take in responding towards climate change effects such as food insecurity and sea level rise. Many countries are attempting to build more resilient societies and economies. Most importantly, adaptation actions acknowledge climate change as a threat that happened instead of a vague idea that might happen in the future.
It is necessary to differentiate between mitigation and adaptation because both sees climate change from different perspective and thus will result in different actions taken.