Well, in the US Armistice Day was established to observe the end of World War I ("the war to end all wars.") I grew up knowing about the significance and solemnity of "the 11th hour of the 11th day of the 11th month," and flags were flown at half-staff that day. November 11th. Some decades ago, after WWII, Armistice Day was combined with Veterans Day and now is observed as Veterans Day to honor veterans of all US wars. For a few years Veterans Day was in October, but then was combined with Armistice Day and called Veterans Day for both world wars and later I think it included the veterans of Korea and Vietnam.
Memorial Day is specifically to honor veterans who died in wars. When I was a child in the South there was Confederate Memorial Day, that was before the Centennial of the Civil War. That was in late April; the end-of-May holiday was "National Memorial Day." I haven't heard mention of Confederate Memorial Day in ages; maybe it is still observed, all I know is that way back in the 1960s we suddenly weren't allowed to play "Dixie" anymore in band, so maybe Confederate Memorial Day went the way of the song.
Does Remembrance Day in the UK honor all veterans, living as well as dead? Just wondering.