A premise pilot, as its name suggests, is a TV pilot that establishes the premise of a show. In the Lost pilot, for example, the plane crashes on the island, and the passengers are lost.
A non-premise pilot is one that feels like any other episode of the show. South Park’s pilot is about Cartman getting probed by aliens. This episode could have been episode eight, and episode eight (or any other episode) may as well have been the pilot.
There are also soft premise pilots, in which the series is kick-started by an event in the episode, but the episode is just like any other in every other way. An example of this is the Friends pilot, in which Rachel arrives at Central Perk in a wedding dress, having just run away from the alter. She reunites with Monica and joins the group. It’s a premise plot, but the way it unfolds is indicative of how episodes play out routinely.