I did some research. They seem to overlap and I am not clear how to differentiate between them. Can you please explain the difference?
Yes you are right to some extent. The term yoga, as used popularly, refers to a system of disciplines exercises for the body and the mind. These exercises or disciplines are largely based on the text written by Patanjali in second century B.C.
The yoga as per Patanjali, which is called more specifically as Raja Yoga, consists of eight component parts or limbs. Among others these include:
Asanas: These are physical postures.
Pranayam: This involves different types of breathing exercises and breath control. I believe the breath control mentioned in the question refers to this part of yoga.
Meditation: This is named as dhyana by Patanjali, and has has become zen in Japanese language by mutation.
It is important to note that though pranayam is an independent arm of yoga, practice of asanas and meditation also requires some regulation of breathing.