No, that's the monarch (where it still exists) or the president in parliamentary democracies (not presidential democracies).
The PM is in fact the leader of government and relies on the good graces of the governing party or parties, not unlike the US president candidate effectively needs to unite his party behind him.
The difference is mostly the ability to get removed/replaced hy his party but usually no term limits, where presidents are term-limited and there are explicit regulations how the parliament can remove them (something that is already inhently given in parliamental systems where the government leader is selected via parliamental majority in the first place).