The word "government" simply has several distinct meanings in English. It can mean the cabinet, the whole state apparatus, or the way the political process is organised. It can therefore come close to being essentially synonymous with "political system" or have a different meaning entirely.
Commented May 16, 2016 at 15:27@Relaxed to add to this, there is also "government" as it is used in social theory where it has a more general meaning referring to (not necessarily political) means of control.
Commented May 16, 2016 at 21:18A Government is an entity that governs a certain group of people. One of its main distinguishing features is the monopoly on the legal use of force.
A Political System is a general set of principles, ideals and limitations that are followed by a government regardless of the more specific goals of that particular government.
For example, we can say that even though the Democrat and Republican parties have vastly different goals, they both follow the general outline of Democracy as a political system when they're in control of the government(this is oversimplifying it of course, but I think it's not necessary to go into detail).