For instance in Germany, the specific words "Bundesregierung" (Federal Government, or just short "government") and "Landesregierungen" (State Governments) explicitly describe the "executive part" of the "political system".
The Federal and State Parliaments are the "legislative part" and the courts are the "judiciary part" (with the "Federal Constitutional Court" at the top). This whole idea of strict separation of power is the most important foundation of the German political system.
When talking about "the government" in Germany, people mean the institutions of the executive (mainly the chancellor and ministries, sometimes also including the president, but never the parliaments and courts).
And tbh, I would also have a hard time describing the US Democratic Party as the "current US government" just because they're sitting in the Congress.