So, I assume that the LDS is managed by the Prophet, similarly to how the Catholic Church is managed by the Pope ?

If memory serves, the President of the (LDS) Church, his advisors, and the members of the church's senior leadership council (called the Quorum of the Twelve Apostles) all hold the title of prophet -- specifically "prophet, seer, and revelator". That doesn't necessarily carry all the implications that "prophet" might outside of an Mormon context, though. One of the quirks of Mormonism is a certain degree of rank inflation compared to most Abrahamic religions; almost all male Mormons enter what the religion calls an order of priesthood at the age of twelve, for example, and a second when they reach eighteen.

But yes, for most purposes the President of the Church is loosely equivalent to the Catholic Pope. Things get a little funky as you get into lower ranks: the LDS org chart is much more complicated than the Catholic, with several layers of leadership councils and more titles than I can easily keep straight. Though it hasn't developed the numerous unofficial and semi-official leadership roles that Catholicism has, being a smaller and younger religion.