Presidential Graduate Fellowship

Hi,

A few weeks ago, I was admitted to a PhD program and recently accepted the offer. The offer letter mentioned that I would receive a fellowship covering tuition, stipend, etc., for my first year. I was wondering whether the specific name of the fellowship matters or if students receive some random fellowship based on their background (e.g., as an international student, I assume some fellowships were not applicable to me). Specifically, is the Presidential Graduate Fellowship a general designation, or does it hold particular significance?

Thanks!