Yes, its true the Sun is your vitalizing core and in addition there is the Moon which is another luminary, and the other 10 planets that signs occupy.
I would like to dispel this myth ~ you are NOT just your Sun Sign. What is more true is that you contain all of the 12 signs and each of these signs correlates to an area of your life.
For example, you may have been born under the Sun sign of Aquarius and you may not have any planets in the sign of Cancer. However, the sign energy of Cancer is still a part of you and will occupy some area of your life. Lets say, this Cancer sign energy occupies or sits on the cusp of the 7th house of your chart, which relates to one on one relationships and/or the marriage house. The qualities of Cancer will usually apply there. Since the Cancer energy is associated with home, mother, nurturance, a wanting to fee safe; you are likely to want to nurture your partner, be mother to your partner or want you partner to mother or nurture you.
We are whole and complete, so it makes much more sense that we would contain all of sign energies.
The value of the natal chart consultation, it that it shows you your unique and individual souls design and learning in this lifetime.
Astrology ~ such a fabulous tool!