The term is most frequently used in formal or semi-formal contexts, especially when discussing government, state-owned enterprises (SOEs), and large institutions like universities or hospitals.
In Government: It's standard terminology. The mayor is the “一把手” of the city government's executive branch, and the Party Secretary is the “一把手” of the local Party committee (and often holds the true power).
In Business: In large corporations, especially state-owned ones, the Chairman or CEO is the “一把手”. In smaller private companies, people are more likely to use “老板” (lǎobǎn), but “一把手” can be used to emphasize that someone is the absolute top boss of the entire enterprise.
Connotation: “一把手” is generally a neutral term that describes a position. It carries a sense of significant power, authority, and responsibility. It is not slang and is used in everyday conversation as well as in news reports.