What is the difference between samadhi and samatha? I am in the habit of getting the concepts samatha and samadhi mixed up. To me they seem like related or even similar concepts. Is that correct? My understanding is that samatha seems like the process of integration and samadhi seems like the result of integration. Is that the correct interpretation?

As a related point are the underlying concepts related if you consider the Pali origins of the words i.e. do they have similar roots in the language?
Samatha is tranquility meditation, meditating on a stable object with the objective of reaching calm states/jhanas.  

Samadhi is concentration. The Buddha's teachings of the eightfold noble path are divided into three categories; sila (morality), samadhi (concentration), and panna (wisdom/understanding). 

Samadhi is the meditation portion of the Buddha's teachings (Right Effort, Right Mindfulness, Right Concentration) and would include Samatha plus other types of meditation.