They are entirely different prayers.
The Rosary was given to us as a prayer directly by Our Lady (in a private revelation, of course) many centuries ago and has been widely described as one of the most outstanding private prayers of the Church (there are actually papal encyclicals that speak about it, and I recommend the book “The Secret of the Rosary” by St. Louis-Marie Grignon de Montfort. The power of the Rosary has been emphasized by Our Lady in successive private revelations acknowledged by the Church (especially the apparitions of Fatima). We should pray the Rosary daily, as often as possible, even if just one decade at a time. The Rosary goes hand in hand, so to speak, with the Scapular of Mt. Carmel.
The Divine Mercy chaplet is another kind of prayer, given in a private revelation by the Lord to S. Maria Faustina of the Blessed Sacrament around 1930. It is also a wonderful prayer, recommended at 3:00 every day, which is the hour at which the Lord gave up His spirit on Calvary for the salvation of mankind, the hour of the divine mercy of God. In no way it can replace the Rosary (though I do pray it more often when I’m not at home since it’s shorter

). You can definitely use a Rosary to pray the Divine Mercy chaplet (and many other wonderful prayers).
Usually the Rosary is prayed either in one decade (one mystery), 5 decades (5 mysteries), the recommended use, since each day has its own assigned 5 mysteries, and rarely the whole 15 mysteries (or 20, if we consider the luminous mysteries added by the Holy Father in the past century). Do remember to add the Fatima prayer at the end of every Gloria, at the end of every decade:
O my Jesus, forgive us our sins, save us from the fires of hell, lead all souls to Heaven, especially those most in need of Thy mercy. Amen.