A theme is a pre-built structure, while a framework is a set of standards to build a TBD structure from. Think of a pre-built house. A Magento theme is similar in that the house is already complete. It has two stories, three bedrooms and two bathrooms. The front door is red and on the right side of the house while the garage is on the left side of the house. With the pre-built house, if you want the front door on the left side of the house there is a lot of work to move it and patch in the old door opening.
A framework, on the other hand, is more like a modular custom home. The floor, doors and windows are in a pre-built library and allow an engineer to build the home with modular pieces once, from the ground up. It's a better way to build frontends that keep them faster and less buggy.
If budget requires a pre-built Magento responsive theme then this can be done; however, we would suggest that if there will be a large number of structural and UX changes, the budget should be increased in order to build with a framework like Bootstrap.