From here you can see better that the mountains are little islands in the ice. [View the larger picture here.] Those islands are called nunataks, and from a biological perspective, they really are like islands, with related but unique ecosystems.
There are a number of huge icefields in Alaska, like the Harding Icefield we were next to. I don't actually know what the technical difference between an icefield and a glacier is (please tell me if you know!), but I think the essential difference is that an icefield is not hemmed in by the landscape... it is the landscape. A glacier might flow between mountains or ridges, while an icefield looks like a sheet of ice with bits of land sticking up occasionally.