Remembrance Day is recognised by the Commonwealth countries and a large part of mainland Europe, and thus constitutes the nearest thing to an international day to remember those who fell in wars past.
Veterans Day is a US only day as far as I know.
Veterans Day used to be known as Armistice Day in the USA as well. Just as in Great Britain, the Commonwealth countries and France after the WWI "Armistice". The USA fought in WWI you know. To the bloody count of about 4.3million men in uniform, 126,000 killed and 234,000 wounded. The British like to claim that America showed up with too little, too late, but it was welcome nonetheless and compelled the Germans to sue for peace. November 11th. was henceforth known as Armistice Day in the English speaking world until WWII.
After WWII, "Armistice Day: was a bit of a euphemism considering that it wasn't an armistice at all, but only a cease-fire. This point is brought poignantly home when visiting the UK. In many English town squares can be seen an original WWI, or "Great War" Memorials with the memorial of those lost, 20 years later in WWII, added atop the first as a sad amendment. Now, Armistice Day is "Remembrance Day" for Brits, Canucks and ANZAC's.
It is "Veterans Day" in the US, for the living and the dead, because we have a "Memorial Day" in May for the dead and the living.
"Memorial Day" was officially proclaimed on 5 May 1868 by General John Logan, national commander of the Grand Army of the Republic, in his General Order No. 11, and was first observed on 30 May 1868, when flowers were placed on the graves of Union and Confederate soldiers at Arlington National Cemetery."
In regards to the Red Poppy's:
In 1915, inspired by the poem "In Flanders Fields," Moina Michael replied with her own poem:
We cherish too, the Poppy red
That grows on fields where valor led,
It seems to signal to the skies
That blood of heroes never dies.
"She then conceived of an idea to wear red poppies on Memorial day in honor of those who died serving the nation during war. She was the first to wear one, and sold poppies to her friends and co-workers with the money going to benefit servicemen in need. Later a Madam Guerin from France was visiting the United States and learned of this new custom started by Ms.Michael and when she returned to France, made artificial red poppies to raise money for war orphaned children and widowed women. This tradition spread to other countries. In 1921, the Franco-American Children's League sold poppies nationally to benefit war orphans of France and Belgium."
So you see, the Red Poppies of "Remembrance Day" originate with the American Civil war and subsequent traditions that came out of that conflict. Not Canada and Europe.
"GOOGLE" should have "poppied" their logo in the USA after all.