What is the difference between samadhi and samatha?
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.