Ancient Free and Accepted Masons versus Free and Accepted Masons
From 1751 to 1813 there were actually two Grand Lodges in England. The difference in A.F. and A.M. vs F. and A.M. states in the United States goes back to a disagreement between these two Grand Lodges in London at that time.
One group was called the "Moderns," but was actually the older of the two English Grand Lodges. The other group was called the "Antients," which became the "Ancient" in A.F. & A.M. The reasons for these separate grand bodies were numerous and would take many pages to explain. The differences centered around perceived changes to ritual work and the inclusion or exclusion of the degree work that is now contained within the Chapter of Royal Arch Masons, an appendant body.
Due to this disagreement, the two groups broke into separate Grand Lodges. The disagreement was later healed around 1880, but by that time, there were lodges and Grand Lodges all over the United States that were descended from one group or the other, and so each group kept their coreesponding initials with which they were formed, (this is also the reason for which there are small differences within different states' ritual wording and Grand Lodge By-Laws and procedures).
Most Grand Lodges in the U.S. recognize each other and treat each other's members as valid Masons.
Also, all of the U.S. Grand Lodges recognize (and are recognized by) the official Grand Lodges of England, Ireland, Scotland and the Grand Lodges in most of Europe, Asia, Africa, South America, Thailand, India, etc.
So, what is the difference between Ancient Free and Accpeted Masons, and Free and Accepted Masons and the members of Accepted Free Masons states and Free and Accepted Masons states? They few intrinsic differences are minimal.
While both A.F. & A.M. and F. and A.M. states exist, along with A.F.M. and F. A. A. M. in the District of Columbia, (with small differences in ritual wording, some officer titles, etc.) in essence, these minimal differences are not as important as the shared brotherhood between all of these groups within the fraternity.
Ancient Free and Accepted Masons:
The 25 A.F. & A.M. states include: CO, CT, DE, IA, ID, IL, KS, MA, ME, MD, MN, MO, MT, NC, ND, NE, NH, NM, OK, OR, SD, TX, VA, WV, and WY.
Free and Accepted Masons
The 24 F. & A.M. states include: AL, AK, AR, AZ, CA, FL, GA, HI, IN, KY, LA, MI, MS, NJ, NV, NY, OH, PA, RI, TN, UT, VT, WA, and WI.
Ancient Free Masons
There is one A.F.M. state: SC.
Free And Accepted Masons:
The District of Columbia is F.A.A.M.