During the periods of the American Revolutionary War, and War of 1812, it's obvious the two nations weren't on the best terms, and by WW1, they're pals. When in this nearly 100 year time frame did the US and UK bury the hatchet?
I think calling them pals is fairly strong. Certainly the relationship was better than before but it was still a relationship of helping each other when their interests aligned.
America did not enter the war until 1917 and benefited from the war by seizing trade opportunities the occupied UK was too busy to take. Germany’s actions were both a threat to the UK (arms race, worries over colonial ambitions ect) and the US (Zimmerman telegram, unrestricted U-boat attacks). America and the UK became closer as both had a vested interest against Germany - nothing bonds better than joint opposition to something else.
So to answer your question, I would say over time the interests of the two nations changed from the revolutionary war period (clearly on opposite sides) to the first world war (on the same side) with the fair amount of the change coming to the later half of your time frame.