Perspectives:

Answer 1

The honouring of those who served and lost their lives while serving their country is common to both and should be regardless what crap is blurted out by some of those enjoying the freedoms they sacrificed for.The US Memorial Day is a day for Americans while ANZAC Day is a day for Australians and New Zealanders i.e. two different countries.

ANZAC Day is also day when both Australia and New Zealand functioned as countries separate to the United Kingdom. It was evidence of the birth of nationhood for both albeit in bloody and murderous way.

They were no longer colonies, they demonstrated the resilience and independence that separated them from the UK. Admittedly, they still had their training wheels on and were not allowed to leave the yard but they demanded respect after 25 th April 1915.

The significance goes beyond the courage and sacrifice to the birth of separateness and respect for both Antipodean countries. That may be the difference otherwise little else.

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Answer 2

This question, What is Australia's equivalent to Veteran's Day/Remembrance Day in the US?, is similarly easily answered with an internet search but I feel some extra context is needed because there will be more than a few Americans who don’t realise the origins of Remembrance Day

What the American’s call Veterans Day is a re-labelled version of Remembrance Day. From an outsider’s perspective, it seems that currently in the USA it’s a time to celebrate any US military person and “thank them for their service”…
In America, it was originally Armistice Day, a time to contemplate the Armistice (the end of the Great War) and what it meant for the future of humanity, but the concept was changed after the Korean War to honour US military veterans.
The US already had a day to honour those fallen in US military service, Memorial Day so the change from Armistice Day, a day when the dead were honoured, to a day where the survivors of the wars, the veterans (when being a veteran actually meant you had served in a war, not simply served in the military), were honoured, was a logical step to avoid having two national days of mourning.

Australia recognizes Remembrance Day. Remembrance Day originates in a ceremony to honour the dead of World War One but has since expanded for some nations to also be a recognition of the Armistice.
In Australia (like other British Commonwealth countries). it is a time to reflect on the sacrifices made by people (military and civilian) during the wars that the nation has been involved in since the Great War (AKA World War One) but we also include those conflicts from the time before the Australian States amalgamated under the Federal entity of the Commonwealth of Australia.

It is a time to honour the dead and the injured, the sacrifices made. It is not about celebrating someone being in the military.