If it is specified as Rashi then it means Moon sign and if it is specified lagan that means the sign that was rising at the time of Birth. Contrary to western astrology we follow the Moon. Western astrology follows the Sun. The difference in simple terms is anyone born for example from 23rd July to 22nd August is Leo. Irrespective of morning hours or evening hours etc. In Vedic astrology we have the 12 signs in 24 hours. That means approximately every 2 hours the lagan or the rising sign changes. The rising sign determines the luck, fate, health , destiny of the individual. The Moon signifies the mind or his thoughts.
Needless to say that there is very big role of Sun in Vedic astrology as it is considered the Soul of a person. What a person desires in his /her life is determined from the Soul. The panchang that we follow regularly for festivals, fast and auspicious dates has strong influence of Sun.