The categories matter because they hold clues to the long-term nature of the relationship. If an expense is temporary or intermittent, there is no long-term component. If it's in a category with operational expenses, then it's more likely that there's budget for next year and the year after.
Having said that, there's a difference between what you put into "operations" and what I do. And the same is true with your client. So you can't assume that you know what they're thinking even when you know where your services fall in their budget.
So, in addition to finding out where you are in the client's budget, you need to ask explicitly what that means to them. All of this is part of an ongoing discussion about your relationship. It's tied into your quarterly "Roadmap" meetings or quarterly business reviews.
In the big picture, there's no excuse for mystery between you and your clients. No excuse for not knowing whether they'll renew a contract or that you're going to raise their rates.
So much of the anxiety that IT professionals feel about client relationships is built up inside their heads. And that's the result of not having simple, ongoing conversations.