The Enneagram is often associated with G.I. Gurdjieff. While he did use the Enneagram symbol or diagram in his teachings, there were no personality types associated with it at the time.
The Fourth Way
Gurdjieff spoke of three traditional pathways to spiritual enlightenment: through the body (the way of the Fakir), the heart (the way of the Monk), and the mind (the way of the Yogi). Gurdjieff taught that a fourth way combines the three centers of these traditional approaches to produce a more efficient, effective, and balanced approach for waking up. The Gurdjieff teachings are also referred to as the Fourth Way teachings.
The centers of intelligence are an important part of the personality types and map directly to the centers described in the Fourth Way. However, this doesn't mean the personality types came from the Fourth Way teachings. The three centers can be found in many other traditions, theories, and disciplines as well.
The Enneagram as Process
Gurdjieff and the Fourth Way used the Enneagram symbol in a very different way than today's personality types. It was primarily used to understand processes. Steps of the process were generally placed on the hexad of the symbol (points 1, 2, 4, 5, 7, and 8) and additional influences upon that process were placed on the triangle (points 9, 3, and 6).
The process begins at point 9, proceeds clockwise around the circle, and ends or repeats when point 9 is reached again. Along the way additional influences or shock points at 3 and 6 are needed to push the process on to the next steps (the shock point at 3 pushes the process on from step 2 to step 4 and the shock point at 6 pushes the process on from step 5 to step 7).
The Laws of 7 and 3
Unlike the Enneagram personality types, not all the lines of the symbol had the same meaning with the Fourth Way Enneagram. The hexad represented the law of 7 and the triangle represented the law of 3. The law of 7 was sometimes called the law of octaves because an octave was placed on the symbol to better illustrate the law of 7.
The octave begins at Do (point 9) and proceeds clockwise up the scale to Do an octave above (point 9 again).
The law of 3 can be seen at the triangle points where point 9 indicates the start and end of the scale at Do and the shock points at 3 and 6 push the process along.
Gurdjieff and the Enneagram personality types
Some teachers of the Enneagram personality types attempt to correlate the Gurdjieff or Fourth Way teachings with the Enneagram. It's important to note that Gurdjieff had nothing to do with today's personality types. Any correlations made are long after the fact and interpretations of those attempting to make those correlations.
Likewise, some teachers try to apply Gurdjieff's use of the Enneagram symbol to the types. As has been shown, Gurdjieff used the symbol in a very different way than the personality types. Any attempt to apply the law of 7, the law of 3, the Enneagram as process, etc. is simply the interpretation of the person trying to do so and can lead to unneccessary confusion and complications when trying to understand the personality types.