Private non-profit agencies exist for some other purpose than making money (e.g., to serve a charitable or philanthropic interest), but in comparisons of private and public management, "private" is effectively synonymous with for-profit firms, and this discussion will regard them as equivalent.
Broadly speaking, there are two ways in which public agencies and private firms -- and, therefore, public and private management -- can be regarded as different. On the one hand, public agencies can be regarded as serving a higher purpose, namely the public good, rather than simply making money for someone. The phrase "public service ethos" implies such a higher purpose.
On the other hand, public agencies can be regarded as sheltered from the competitive pressures that act on private firms, and thus lacking the motivation for improving efficiency that a competitive marketplace is presumed to generate. The word "bureaucrat," with its negative connotations, encapsulates this latter distinction, in which public agencies are viewed as inherently less efficient -- and public management, at least good public management, as inherently more difficult -- than private agencies and management.
In the English-speaking nations, with their traditions of limited government and suspicion of governmental authority, the latter presumption tends to predominate, with public servants and managers not h