They're often used interchangeably in the real world, but they tend to have more specific meanings when it comes to case studies:

• A structure is the logic and approach by which you crack your problem. As every problem is different in its own way, you'll want a structure which fits. For example, imagine the question is whether Company A should acquire Company B. You might want to look at 4 things (company A strategy, company B market, company B market position and strengths and price). What you don't want to do is just start talking without thinking or knowing where you're going: "Well, company B seems good I guess but it would take time and it's products seem good but..."
• As you mentioned, a framework is generally understood to be a series of steps or topics which you address in order to solve a problem, generally created in academia or business. You never want to use one of these in a case. Recruiters are looking for critical thought and using a "one size fits all" way of breaking down a problem that you read in a book does not help demonstrate it.