Can "Chauvinists" and "elitist" be same?

I was going through GRE vocabulary on magoosh app and it is stated that both have same meaning but clearly

Chauvinist : a person displaying aggressive or exaggerated patriotism.

And

Elitist: relating to or supporting the view that a society or system should be led by an elite.

which doesn't feel same to me.

Can someone please clarify?

chauvinist has a secondary meaning that has become more common in recent years:

a person displaying excessive or prejudiced loyalty of support for a particular cause, group, or gender.

The most well known example of this is "male chauvinist".

This is the sense that is very similar to elitist, because the chauvinist typically believes that their group is the elite group, and should be in charge of society.