Power
All public administrators have some form of power; that's why that word administrator is there―they administrate. But how much power do they have? After all, the President of the United States and your town's Sanitation Manager are both technically public administrators, and while both of them may deal with garbage on a daily basis, only one of them actually has to clean it up.
To find examples of the kinds of powers public administrators hold, all you have to do is look around the city/town/village/space colony where you live.
Typically there's a chief executive of some sort (you might call them a mayor, elder, or overseer) whose job it is to implement whatever policies or plans it is that they or the community have decided need to be a thing. This includes everything from establishing residential planning zones to downtown traffic rules to whether a new skate park gets built.
However, there's only so much the community leader can do on their own, especially considering the main responsibility of the job is finding other talented people and telling them what to do. That means a team of other qualified (we hope) public administrators who specialize in the fields necessary to accomplish whatever thing needs accomplishing.
These include city managers to oversee the zoning, public safety coordinators to ensure things don't break and hurt people, and budget analysts to figure out how it's all going to get paid for.
Each of these people (along with possibly dozens of other lower managers) may have their own team of specialized public administrators, accomplishing even more specific things in order to help make life in their city/town/village/space colony as easy as possible.
Sound complicated? It is; this is often why things sometimes don't get done, or get done very slowly. Why else would a building as important and symbolic as the Freedom Tower take over a dozen years to complete?
So who holds the ultimate power? "Why, The People, of course" says your Civics & Government teacher as they stand on a boulder overlooking the purple mountains majesty.
But it's true―if the people want a thing done, and you aren't able to get said thing done, they'll find someone else for the job. The People are picky like that.