What is the difference between the two births under the two covenants?

In the allegory of Galatians, Paul contrasts the two births signified by Isaac and Ishmael. Ishmael, born of Hagar, symbolizes the natural birth under the covenant of works, which is bound to failure and bondage. On the other hand, Isaac represents those born of the Spirit, who partake in the covenant of grace, characterized by divine promise and miraculous new birth. This new birth is essential for believers as it signifies their transformation and inclusion in God's family, reinforcing the theological premise that salvation is by grace alone and not by human effort.