Preamble
History became complicated if there were multiple kings with same name. As in Maratha History there were four known Chhatrapati. After Shahu I who was fifth great Chhatrapati, Maratha kingdom divided into two thrones, out of them first throne was of Satara and second was Kolhapur. So, list of Shahu Maharaj were either from one of these thrones.
Many people have the confusion in between two Maratha kings. First is Chhatrapati Shahu Maharaj of Satara throne and second is Chhatrapati Shahu IV of the Kolhapur’s throne. First Shahu Maharaj of Satara was the son of Sambhaji Maharaj. Whereas the second King Shahu Maharaj of Kolhapur province was famous as Rajarshi Shahu Maharaj and he was a prominent social reformer as well.
Especially people who knew the name of Shahu Maharaj could not differentiate between those two. So first, I want to clarify it about those two kings.
List of Shahu Maharaj in Maratha History
Shahu I (1682-1749)

He was the fifth Chhatrapati of the Maratha Empire. He was the grandson of Shivaji Maharaj, the founder of the empire. Shahu I was a capable ruler and administrator of Satara throne. He helped to consolidate the Maratha Empire and expand its territories. He also introduced a number of reforms, including the establishment of a regular army and the creation of a system of revenue collection.
In the annals of Indian history, Shahu I, born in 1682, emerges as a visionary ruler whose reign left an indelible mark on the Maratha Empire. Ascending to the throne in 1707, Shahu I was not merely a king; he was a symbol of resilience, reform, and revival.
Early years of Shahu I were marred by turmoil. He was taken prisoner by his half-brother, Ramaraja, and held in captivity for several years. But adversity only steeled his resolve. Upon regaining his freedom, Shahu I embarked on a mission to rejuvenate the Maratha Empire, which had been weakened by internal strife and external invasions.
Shahu I passed away in 1749, leaving behind a legacy of unity, reform, and resilience. His life serves as a testament to the enduring power of leadership, vision, and the indomitable human spirit. Shahu I remains etched in history as a ruler whose legacy continues to inspire generations.
Shahu II OR Rajarshi Shahu Maharaj of Kolhapur (1874-1922)

He was the first Maharaja of the princely state of Kolhapur. He was a social reformer and a champion of the rights of the lower castes. He introduced a number of progressive measures, including the establishment of schools and colleges for the lower castes, and the reservation of government jobs for them. He is also credited with the introduction of the widow remarriage act in Kolhapur.
He was a prominent ruler during the late 19th and early 20th centuries. He reigned from 1894 to 1922 and was known for his social and educational reforms.
Shahu III

There is not much information available in his account. But he probably ruled as titulary Chhatrapati of Satara throne. His reign was from 1925 to 1960.
Shahu IV
His full name was Shahu Chhatrapati Shahu Maharaj Bhonsle, was the ruler of the princely state of Kolhapur during the post-independence era in India. He ruled from 1947 to 1983 and was known for his role in the integration of Kolhapur into the Indian Union and his efforts in social and educational reforms in his state.
Popular Shahu Maharaj in Maratha History
Out of four the Shahu I and Shahu II was very popular. Shahu I was popular because during his reign kingdom became empire. Its possible because of brave Peshwa Bajirao who was general of Shahu I.
On the other hand, Shahu II was famous because of his work in educational sector and other social reforms. Due to his social work. Kurmi Kshatriya Sabha entitled him with Rajarshi.
So when you heard of Shahu Maharaj from Maratha History. Then, mostly it refers to one of above Shahu Maharaj. This article help you identifying which one is the source referring to, because I found there were so much confusion on internet among those two.