The city says a department is getting more money and residents say it is being cut

I attended a city budget presentation where an official said a department would receive more money next year. That evening, a neighborhood group posted that the same department was facing a cut. Both sides linked to official documents.

At first I assumed one was lying. Then I opened the links and found several possible baselines. The proposed dollar amount was higher than the current adopted amount, lower than an earlier request, and possibly lower after considering the cost of maintaining the same service. One document counted a temporary grant separately. Another folded some staff costs into a central account. The word "cut" was doing enough work for an entire department.

I am not trying to settle the local dispute here, especially without naming the city or documents. I want a method for asking what each claim compares. More than what? Less than what? In nominal dollars, staffing, hours, locations, or service delivered? Does the comparison include temporary money? Has responsibility moved with the money, or did only the account code change?

The official presentation emphasized the proposed increase from the adopted budget. The advocacy post emphasized the gap between the department's request and the proposal. Each comparison may be accurate while answering a different question. The public argument becomes misleading when either baseline is presented as the only possible meaning.

I am planning to make a small table with the current adopted amount, actual recent spending if available, the department request, the executive proposal, and the final adopted figure when it exists. Beside each I would note major one-time funds and any change in responsibilities. I would avoid adjusting for anything I cannot source from the budget materials.

What else belongs in the comparison? And when is it fair to use the ordinary word "cut" rather than the more cumbersome phrase "less than the requested amount"?