In male horoscopes, Mars and the Sun represent the individual expression of masculinity and fatherly qualities. In female horoscopes, these traits are instead projected upon world and the surroundings in the form of expectations and desires. Hence, Mars and the Sun in female natal charts represent what a woman look for in men, what she is (consciously or not) drawn to. In the real world things are of course not that simple, and the totality of indications by which women are attracted to the opposite sex amounts to a lot more than only the Mars and Sun archetypes. That being said, these two taken together with the close aspects they make with other planets is a reliable benchmark to begin with.
In a wider sense, the Sun and Mars manifest qualities that are likewise present in the woman herself; her animus, if you will. Much of the inherent meaning of these planets is common to all people, yet traditional astrology has often associated the Sun and Mars symbolism in a woman's chart with other people in the woman's life, namely fathers, brothers, husbands and male relatives. I don't think this approach is wrong, but it is decidedly limited and in itself less than satisfying as a means to interpret the big picture.
What is then the actual difference between the Sun and Mars as guidelines for what attracts a woman? The planet Mars is a dynamic, not-so-subtle force, in many ways directly physical-sexual in nature. Hence it will have a greater influence in determining what "turns a woman on", what enlivens her senses and heats up her passions. This primarily sexual reaction can be passing and shallow, but is usually strong when experienced. The Sun is more subtle, yet wider in scope. It has physical, emotional, mental and spiritual ramifications and might contribute a sense of admiration and belonging.
Let's imagine (for the sake of simplicity) a woman whose Mars is in Libra, closely aspecting the planet Venus. The same woman's Sun is placed in Cancer, in close aspect with the Moon. We can expect this woman to often get turned on by Libra-governed, "venusian" men. Charming, polite, suave and sophisticated may be the path into bed with this woman. On the other hand, the kind of personality she feels a deeper or more long-lasting bond with might be quite different. Here, the emotional, introvert soul-child that characterizes a Cancer-born (or strongly Moon-dominated) man pulls the woman in another direction, which is also strong albeit different. Is it a classical case of being sexually attracted to one person, versus a deeper sense of kinship and feeling of belonging with another? Possibly.
You might want to ask the question of how Mars and Sun work in lesbian / bisexual astrology maps. I personally believe they share the same symbolism and influence, while lacking the motivating, action-guiding power they possess in heterosexual charts. Mars and Sun represent the same archetypes to homosexual women, but they remain romantically powerless. That is not to say the masculine has no influence over a gay woman. Indeed quite the opposite, considering the fact that a lesbian woman might be more likely to actively express these masculine energies in her everyday life.Next time: Venus and Moon in the male horoscope!