I cant speak about usa, too big, too far away
But while Aus and NZ both had many similar words ie essential workers, Australia was more relaxed. For instance, the line between essential and non essential was drawn between hairdresser and beautician.
So in Australia, hair dressers were considered essential, so they could stay open. You are welcome to go out for an essential service such as getting your hair cut. A hair dresser's child was welcome to go a school even though school was kinda closed. Not so in NZ, even a kid losing their ball onto their neighbours yard, the neighbour was not allowed to return the ball!.
Very similar per capita result between NZ and Australia, but the strictness of the supression/lock down was quite different.
Like captain america saying 'i can do it all day long' ( and not look shaggy) Australia can maintain its current suppression for the next 6 months and not look too shaggy.
(Ps it was quite contentious drawing the line in the sand between hairdressor and beautician) but the line seems to have been appropiate for this country's particular situation. Resourced test/trace & isolate is a technique not a strategy, but perhaps as a technique it seems effective to making australia's strategy work in Australia.