Hey!
They are very similar questions, but not quite identical!
"Why our firm?" is broader, and focuses on what attracts you to the firm as an organisation - for example, its practices areas, clients, strategy, culture, recent deals, etc. You are essentially showing that you have researched the firm and understand what makes it distinctive, and can then show why you are a good fit for the firm based on your motivations and skills.
"Why do you want to train at our firm" is more personal, and focused on fit - for example, why that specific training contract structure, seat system, support available, and environment suit you and your development. They will want to see how the firm aligns with your goals and how you see yourself there as a trainee.
In practice, there is a lot of overlap and many candidates will use similar core points for both (e.g. you might want to join a firm due to its training structure). However, I would slightly tweak the emphasis for each answer.
As for whether both would be asked, I imagine it is possible, but likely uncommon. More often, interviewers will ask one and then probe deeper with follow-up questions (e.g. "why is that important to you?")