Hi,
If by 'business case' you refer to a written case format, yes indeed that is slightly different from the classical consulting case which is 'live' and dynamic throughout the entire time.
In a written format, normally you are either given time before the interview or during the interview to process the information, come up with a short presentation and then discuss the findings with the interviewer(s).
To be honest, I find that many people over-index on the differences in the formats.. fundamentally any consulting firm is going to look for the same traits in candidates.
Arguably the biggest difference to me is in time management and understanding how to structure what you are eventually going to present. Some people worry about communication (i.e. slide writing/presentation) but to me if you are clear in thought you will be clear in presentation, at least in the context of the interview.
If you would like to practice a written case or 2, let me know, happy to connect and discuss further.
All the best!