Like anything in Freemasonry that goes back to that period the answer is not so simple. The short version is that it has to do with the schism between the Moderns and the Antients (Ancients). The first grand lodge formed in 1717, the Premier Grand Lodge of England, known as the Moderns, became F&AM. The competing grand lodge formed shortly after, the Most Ancient and Honourable Society of Free and Accepted Masons, known as the Antients, became AF&AM with the addition of the "ancient" to their name. Both of these grand lodges were chartering lodges here in the New World at the same time. When the two competing grand lodges settled their differences and formed the United Grand Lodge of England the difference in F&am and AF&AM became moot as grand lodges in the United States moved forward. Note, there are two jurisdictions in the United States that are neither. South Carolina is AFM and the District of Columbia is FAAM. This is of course for mainstream lodges and Prince Hall is another subject. Search for articles on the schism between the two early grand lodges. It is some interesting reading.
As for the Confederation Masonic Interamerican, I believe that organization is a confederation of jurisdictions and does not itself make Masons. I could be wrong as don't know enough about them. But I am pretty confidant that no US grand lodges are part of CMI and instead coordinate through the Conference of Grand Masters of Masons in North America (COGMNA). There are Brothers on this forum that can speak better to that.