Feel free to use any synonyms to buckets - e.g. 'I'd like to investigate the following x areas/issues/topics/......'. Your interview won't really mind about the specific word you are using, I will be interested a) in your 'buckets' and b) how you communicate them (in a rigidly structured, logical way..).
For looking more closely at laying out a framework, let's distinguish 2 parts of a typical case interview where frameworks usually apply:
1) Structure for the overall case at the beginning of the case interview
2) Answering specific questions in later stages of the case interview
ad 1) Structure for the overall case at the beginning of the case interview
This is when you typically need to develop an overall structure on how you want to tackle this case. Interviewers often ask something like "What are the issues you need to consider here?" or "Let's assume you are the project manager of this consulting assignment - which areas would you like to investigate?".
It is highly unlikely that you will be able to fit a realistic case interview question into a standard framework - if it would be that easy, nearly all candidates would make it into the top management consulting firms, and clients could solve their business problems without paying millions of dollars to consulting firms by simply applying a standardized framework.
So, whatever your approach will be, it needs to be very flexible because you will need to adapt it to a huge extent to your specific, individual interview question. And yes, it is your approach which needs to be flexible to make it fit to the case question, and not the other way round.
(This is exactly what case interviewers hate when candidates use standard frameworks – when candidates use the framework as they are, and try making the case question fit to the framework instead the other way round. Otherwise, nothing is wrong for case interviewer when you are using standard frameworks!)
In general, I can see two different approaches for this stage of the case interview:
Approach #1: Get your hands on some overall case interview structures (like Victor Cheng's Case Interview Frameworks slides, and in addition it is worth reading Victor Cheng's approach on case interview frameworks on his website).
Approach #2: Based on your case interview experience (i.e. having solved dozens of case interviews and having read through even much more of them) you can also try to develop the first level of your case interview structure (or in other words, the main areas or buckets you want to investigate) 100% individually from scratch. It probably really takes a lot of experience to do this well – but the good thing is that you can easily combine this approach #2 with approach #1 at any time!
Whatever approach you are using, this will mainly get you to the first and second level of your structure. However, this won’t be enough to impress your interviewers – depending on the specific case question, it is usually favored to have at least one more level of structure.
And exactly for this additional level, knowing the most common business frameworks and concepts is extremely helpful to all candidates. It is just so much easier to further structure your case interview if you don't have to start from scratch, but can apply existing frameworks and concepts. And even though you might be able to use maybe only 60% or 80% of a framework and need to adapt it to make it fit to the specific question, you are nevertheless already far ahead than if you would need to develop all that from scratch.
Given the high mental pressure and time pressure in a consulting case interview, it is extremely difficult even for the best candidates to come up with the right issues, and at the same time remaining structured in a MECE way – this is just another reason highlighting the advantage of knowing the most important business frameworks and concepts, as they will not only help you to come up with a structure at all, but keeping it MECE and saving precious time in the case interview as well.
ad 2) Answering specific questions in later stages of the case interview
For answering specific questions later on in the case interview, it is as important to remain structured in whatever you say as in the beginning of your case. Sometimes it might be well enough to use internal vs. external, short-term vs. long-term, pro vs. contra and similar basic structures, but more often than not this will not differentiate you from other candidates (merely solving a case is usually not enough, you need to impress your interviewer by clearly standing out from the crowd of other applicants).
Also here, knowing standardized business frameworks and concepts comes in very handy. As opposed to the overall case interview question at the beginning, most questions later in the interview are much more focused and narrow - therefore chances are higher that you can use a standardized business framework to a very large extent just as it is to answer the question.
For structuring case interviews, I actually wrote an ebook which helps candidates to understand the most commonly used and thus most important frameworks you should be familiar with, and also how to apply them on a real-life-case step by step. You can find the ebook here in case of interest: http://cif.consulting-case-interviews.com/
Hope that helps - if so, please be so kind and give it a thumbs-up with the green upvote button below!