To understand the difference between these two it is first important to clarify the definition of Yoga and Meditation.
Yoga is a holistic system created by the ancients. It offers us an opportunity to break out of this ‘matrix’ of illusion that’s the visible universe around us. This science is thousands of years old and is not restricted to just Asanas as is the popular belief.
Asana as Hatha Yoga and Meditation as Raja Yoga
However ‘Yoga’ today can mean either Hatha Yoga (Mastery over body ~ Asanas) or Raja Yoga (Mastery over mind ~ Meditation). All forms of Yoga that focus on physical asanas are derivatives of Hatha Yoga with different brand names (e.g Jivamukti or Sivananda). Likewise Raja Yoga covers most forms of meditation with the ultimate goal as Samadhi.
The earliest known texts that actually document the range of physical asanas are Hatha Yoga Pradipika or Gheranda Samhita. Written between 15th and 17th Century, these medieval texts are the foundation of modern Yoga. The earliest known text on Raja Yoga philosophy is Yoga Sutras of Patanjali which is 2500 to 5000 years old. So it holds more gravitas and authority as the original resource for Yoga.
Meditation in the Principles of Ashtanga Yoga
Raja Yoga is the practice of the eight principles of Patanjali’s Ashtanga Yoga. This is different from the Mysore brand name ‘Ashtanga Yoga’ which is a Hatha Yoga sequence). In this philosophy before the practitioner can even begin the practice of Asana or Pranayama, he/she must purify through the first two practices of Yamas (morals) and Niyamas (ethics).
The seeker starts the third stage of Asana siddhi after purification through moral restraints and ethical observances. Patanjali has dedicated only one sutra to this stage as follows ~ Sthira Sukham Asanam (Stable and Comfortable Pose). Because only in being still can the body move on to the higher practices of Raja Yoga.
Therefore all Hatha Yoga Practices aim to help us achieve this one ability to sit still and meditate. The goal of asanas was never to help us protect from diabetes or heart diseases, they simply aimed to give us the best possible health so we could pursue our spiritual practices. The end goal of Hatha Yoga is Raja Yoga and the end goal of Raja Yoga is Samadhi.
So there is no difference between Yoga and Meditation, both are a part of the process that leads to the ultimate goal of ‘Enlightenment’. There is no yoga without meditation, there is no meditation without yoga.
I originally answered this question on quora.com