"After 1865 these was only one army for the one government, and no need to distinquish it from any another army operating on US soil, therefore today we commonly refer to the army of the USA as the AMERICAN army."

I've NEVER heard of such a reference. Did you take a breath while you were typing that? Today things are distinguished by "navy", "marines", "air force", and "army". The problem with this subject and this discussion in general is emotion and heritage. Let's remember the terms Army of Northern Virginia, Army of the James, Army of the Potomac, Army of Tennessee, etc. There was a lot of regional divide back in those days.... JackO