The American military adapted most of its rank insignia from the British. Before the Revolutionary War, Americans drilled with militia outfits based on the British tradition. Sailors followed the example of the most successful navy of the time -- the Royal Navy.
So, the Continental Army had privates, sergeants, lieutenants, captains, colonels, generals, and several now-obsolete ranks like coronet, subaltern and ensign. One thing the Army didn't have was enough money to buy uniforms.
To solve this, Gen. George Washington wrote, "As the Continental Army has unfortunately no uniforms, and consequently many inconveniences must arise from not being able to distinguish the commissioned officers from the privates, it is desired that some badge of distinction be immediately provided; for instance that the field officers may have red or pink colored cockades in their hats, the captains yellow or buff, and the subalterns green."
Even during the war, rank insignia evolved. In 1780, regulations prescribed two stars for major generals and one star for brigadiers worn on shoulder boards, or epaulettes.