In the case of Hawaii, it is the oceanic plate that is moving,...

In the case of Hawaii, it is the oceanic plate that is moving, not the hot spot.

The oceanic plates are born at oceanic ridges when hot rocks rise to the surface from deep within the mantle and melt due to decompression melting forming basalt.

At the other end of the oceanic plate will be a subduction zone where the oceanic plate dives underneath the continental crust.

So what you have is oceanic crust forming and spreading outwards from the oceanic ridges and been destroyed or subducted back into the earths mantle at subduction zones.

As the oceanic plate is moving over the hot spot volcanoes will be born last several million years and then die as the plate moves off the hotspot. A new volcano is the born directly over the hotspot. An interesting point is that the Hawaiian volcanic island chain actually has a big dog leg bend in it, rather than been straight. One theory is that the change in direction of oceanic plate was caused by the intial continental collision of plates to form the Himalaya mountain range.

In the case of continental hotspots like Yellowstone park, the hot spot has stayed in the same position and the continental crust has moved relatively very little in comparison, and as a result the whole park is one superheated bubbling cauldron of volcanism.

One final interesting point to note is that earth scientists can use all the known hot spots to measure relative movement of both continental and oceanic plates as the hot spots will remain fixed in the same position and the plates slide around on top.

One question a lot of people ask is why does the oceanic plates sink and continental plates float or slide over the top of the oceanic plates. It is to do with the minerals that comprise each of the plates. Oceanic plates are made up of more iron and magnesium rich minerals which are typically very dense. The continental plates are made up of silicic minerals which are typically very light. SG of continental crust around 2.6 g/cm cubed versus 3.0 g/cm cubed for oceanic crust.

Hope that answers a couple of questions.