Melvis: You are correct. It can be said that in Tarot, the Personality Card is the exterior expression of the individual; how one interacts with the environment & presents the self. It is the aspect that would tend to exhibit the influence of the exterior world on the person. In Astrology, it would be comparable to the action of the ascendant or rising sign.
The Soul Card describes the qualities & the purpose of the soul; its essence in the particular life. In astrological terms, it would be comparable to the Sun sign, which is indicative of an individual's character.
Similar to Astrology where one is more than just the Sun sign but a composition of a myriad of influences from a group of planetary aspects, so is one in Tarot more than just the Personality or the Soul Cards. In deciphering the various correspondences in other cards, it is a means of self-understanding & self-development; a journey into the psyche of individuation & assimilation/wholeness.