I’m confused about the difference between these, too.
In the edit-item page, Type is described with a dc equivalent:
dcterms:type
while Class gets a textual description:
A type for the resource. Different types have different default properties attached to them.
(Note that Class is confusingly defined as a “type”.)
Class appears more prominently overall: it comes near the top of the properties; it’s the one in the standard items view, and it’s a default field in the Resources page. Yet type is the field that shows up on the item page, as @iwaseka notes, and it’s the one with the dc definition.
It’s not clear to me why Class and Type are both there, I guess.
Edit: Just saw DCMI Type Vocabulary in Class and Type