Bhagavad-gita 2.13 Lord Krishna explains that Soul transmigrates while body changes

dehino ‘smin yatha dehe … Lord continued explaining about the embodied soul. As the soul continually passes, in the body, from boyhood to youth to old age, the soul similarly passes into another body at death.

The body continuously changes between birth and old age while the spirit soul remains unchanged. There are six stages of changes in body - birth, child, youth, adult, old age, death. The individual soul however does not transform and finally changes the body at death and transmigrates to another body. Since soul is certain to obtain another body, there was no reason to lament on account of an individual’s death.

A dhira or sober person has perfect knowledge of the individual soul and is not deluded by the change of bodies. He knows that the soul is a fragmental portion of the Supreme and remains the same fragmental throughout his conditioned life. Once liberated, he continues to be fragmental and lives an eternal life in knowledge and bliss with the Supreme Personality of Godhead.

A dhira also knows that Supersoul or paramatma is present in each and every individual body along with the individual soul. The Supersoul is different from the individual living entity. When the sky is reflected in water, the reflections represent the sun or the moon and the stars as well. The stars can be compared to the living entities and the sun or moon to the Supreme Lord.

The individual fragmental spirit soul is represented by Arjuna and the Supreme Soul is the Supreme Personality of Godhead Sri Krishna.