South American Mahogany (Swietenia genus) is the traditional furniture-grade mahogany, and is the original and highest quality wood of all those now called "mahogany".
The fairly closely related African Mahogany (Khaya genus) is often used in boat construction and marine plywood (from what I've seen recently) and can be recognized by it's longer more-open grain compared to SA mahogany. It's not as hard as Swietenia, but still a quality hardwood.
Another genus of African woods sometimes also referred to as "mahogany" is the Entandrophragma genus. That includes a wider variety of woods including some spectacular species such as Sapele which has a broad ribbon-striped figure, along with others which are less notable. I've seen sapele plywood on a couple boats I've been on.
As Guy says, the biggest abuse of the name "mahogany" is when it is used for Luan "phillipine mahogany", as Luan is not at all related to the others listed above.
Personally I think SA mahogany is nearly the easiest of any furniture wood to work with. Certainly more forgiving than the domestic hardwoods like cherry, maple, birch, walnut. The african mahoganies are a bit more varied, some easily workable, others less so.
Nate