Government is a term with multiple senses.

In the US it’s common to only use it to describe the entire apparatus for holding, administering and enforcing state power.

But it can also be used to mean the current ruling power in a parliamentary system together with the administrative bodies under its direct control. So something more akin to just the executive branch in the US system. And then certain state agencies such as the judiciary are meant to be independent of the government under that meaning of the term. I believe this is the most common understanding of the word outside the US.