I understand how parent and child themes work. But my question is how do frameworks fit into it? Are they just technically parent themes you create different child themes from?
You're absolutely right. Frameworks like Thesis, Genesis, and Ultimatum (among others) are essentially barebones themes that allow for modular customization with child themes and skins (in terms of Thesis, though it's been years since I used it, so that may have changed).
I use Ultimatum as a framework for features, for instance, and have child themes to add in all the customization.
"Framework" is just jargon for what is essentially a skeleton for you to build off of. If you're familiar with Ruby on Rails, I think of them almost like
rails g scaffold.