Not the same.

While on the surface this is correct, Cameron subsequently ran as the face of the party in a general election before assuming office, thereby receiving a public mandate (albeit a weak one first time round due to the hung parliament).

May did not.

Her only opponent quit, she was the only one running.

And just like Corbyn. That's the way it's always worked in the UK - we don't have a "president". Amazing how many people don't understand this.