Was Picquery a president or THE president of United States?

Question

In Fantastic Beasts and Where to Find Them movie, everyone calls Picquery "Madam President".

In Britain, there's Ministry of Magic (not Magical Parliament) and the head is called the Minister for Magic (not Prime Minister) who reports to the muggle Prime Minister. It gives me the feeling that the Ministry of Magic comes under the muggle government (only it's hidden).

As wizards already follow lots of muggle things like political boundaries of nations, names of nations/cities etc and they use muggle resources like roads, it looks good to give respect to muggle systems (as wizards can also be called citizens of a nation as they are humans), so even International Confederation of Wizards can enforce it (I am speculating the last part).

Was Picquery president of the Magical Congress of the United States only? Or, was she the muggle no-maj (or, say universal) president of the United States?

Only canonical answers with proper citations, please.

Answer 1

She is the president of MACUSA - not of the USA. (That was Calvin Coolidge in reality and there is no evidence that JK Rowling ever suggested otherwise).

Perhaps the most significant effect of Salem was the creation of the Magical Congress of the United States of America in 1693, pre-dating the No-Maj version by around a century. Known to all American witches and wizards by the abbreviation MACUSA (commonly pronounced as: Mah – cooz – ah), it was the first time that the North American wizarding community came together to create laws for themselves, effectively establishing a magical-world-within-a-No-Maj-world such as existed in most other countries.

From Pottermore's JK Rowling writing on The History of Magic in North America. Here is another quote showing the role of the president.

In 1790, the fifteenth President of MACUSA, Emily Rappaport, instituted a law designed to create total segregation of the wizarding and No-Maj communities.

MACUSA exists in secret and is not related to the US government, and like the UK Ministry of Magic it answers to the International Confederation of Wizards and its Statue of Secrecy.

One final quote from the same source to confirm its independence:

In America, MACUSA acted totally independently of the No-Maj government.

Answer 2

No, MACUSA was entirely separate from the Muggle government in America.

It's possible for there to be complete wizard and Muggle separation between the two populations with their governments still cooperating to hide the existence of wizards from Muggles as is the situation in Britain, so that wizards and Muggles are separated in America isn't necessarily proof that the president might not cooperate with the President of MACUSA like the Prime Minister and the Minister of Magic do.

However, there's a quote in the Pottermore writing on MACUSA specifically stating that the MACUSA had no connection with the No-Maj government.

America remained one of the most hostile environments for magical people, mainly because of Scourer descendants who had vanished permanently into the No-Maj community and who kept suspicion of magic alive. Unlike most Western countries, there was no cooperation between the No-Maj government and MACUSA.