For example Pakistan has a "President " and that does not somehow magically make them a secular state.
We are the "Islamic Republic of Pakistan" (full name). We have never claimed nor pretended to be secular.
As for our President, he has all the powers of a janitor. It's the Prime Minister who calls the shots.
It's based on British style democracy... they have a powerless King, we have a powerless President.
So we are democracy (we have elections) but we are not secular.
USA is NOT a democracy... but is totally secular.
Weird world.
Nooooooooodist....!!!