A prime minister style government is different from a presidential style government and it is not just simply a difference in name.
In a presidential style government, you vote for the president ( maybe not not exactly, but close enough) . In the a PM style government you vote for candidates from your constituency to parliment. The majority party in the Parliament, or a majority coalition, choose a prime minister. Although typically, the party leader becomes the Prime Minister and is often the face of party, during elections. Which is why you hear complains in these places that the election is becoming too presidential.
So at any time during the term, the party or coalition may become dissatisfied of the PM, and force him/her to resign, which what happened to May. Or sometimes the PM him/herself might just resigns after he/her royally fucks up, like what happened with Cameron.
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