Economy lodging is dorm-style housing: the rooms just have bunk beds in them and nothing else. You bring your own bedding and towels (or they can be provided if you order in advance, for an additional fee of $25). Generally, each person will have one bunk bed, so you can sleep on the bottom and keep your belongings on top, or vice versa.
Semi-private lodging is more like motel-style housing: the rooms have single twin beds, dressers, nightstands, reading lamps, closets, etc. Bedding and towels are provided.
In both cases, bathrooms are shared with the rest of the lodge.