Yeah, and by that time there were admirals in the U.S. Navy too. But it’s my impression that for quite some time (until the Civil War era, perhaps), the U.S. military was conscious of avoiding the semblance of titles of nobility.
Ulysses Grant, I believe, was only a lieutenant general, even when he was in command of all U.S. forces.
But what about Major Major? 
What, when the Philippines was a U.S. Territory? How could it have had its own army?
The Philippines was a territory 1898-1935. It then became the first U.S. Commonwealth (à la Puerto Rico’s current status) with the goal of full independence in ten years (the 1934 Tydings-McDuffie Act provided for this). As it turned out, the little incident with Japan postponed that for a year, and it got independence in 1946. As a part of the Commonwealth preparation-for-independence activities, the U.S. maintained military bases at selected points in the archipelago, and provided a highly experienced general with familiarity with the country (MacArthur) to organize and train a Filipino Army. Because MacArthur and Philippines President Quezon were the best of friends in a classic old-boy network manner, he was named CinC of the Filipino Army with that rank.
Life imitating art.
Yeah, some of their photo spreads were a case of Life imitating Art
…Lucely speaking, of course! 
I know that in some Mideast nations crossed swords or scimitars (enclosed by a wreath) are used instead of crossed batons enclosed by a wreath.
You’re going to have to answer for this someday you know.
When I was in the Navy, the XO of my carrier was Capt. Major. We all joked that he never considered the Army as an option.
Here’s a nice picture of Germany’s Generalfeldmarschall Wilhelm Kietel’s baton as he was signing the surrender documents in May 1945.
Linked off of this page.
Hmmm . . . that doesn’t look much like the other field-marshal’s batons pictured in links in this thread; it looks more like a fancy swagger-stick.
