CANZUK is only about a free trading block, Customs duties and other barriers to commerce would be removed for trade between CANZUK nations. Freedom of movement (similar to what NZ have with Aussie) between the CANZUK countries.
But we could also trade together as a block to give the block more bargaining power with the like USA, China, India and the European Union.
Each country is still fully independent, stills makes own laws, and other trade deals with other countries as normal. There is no central government like the EU that is making laws that all countries must follow. Each country remains sovereign and independent. A NZ fishing vessel still "can not" go and fish in Aussie waters and vis-versa etc, which what happens with the EU, and has decimated the UK fishing grounds.
If a government wishes to bail out a national company it can that is up to the government of the day... again with the EU, this has to be passed by the EU and from my understanding has been pretty unfair against the UK.
The idea being that because we are all similar GDP’s per capita which means there won’t be the influx on immigration or any brain drain. This is a problem for the EU as many of the countries the GPD’s per capita are so varied an then you get the migrant flow only going one way.
We all speak english, again the EU how many different languages and dialects.. the more there is the higher the chance and a mistranslation.
Our heritage culture is similar (not the same but similar) ie; for NZ we have really embraced the Maori heritage and culture but the you can still see the here in Dunedin the Scottish and English history. Again look at the EU, 27 countries, at least 27 different cultures, and some of those countries and cultures have sub-cultures...
Some people want to take it a bit further with a tighter defence agreement and have something similar as NATO, as we are all allies anyway and all are part of The ‘Five Eyes’ (FVEY) agreement and CANZUK would just compliment NATO. Two of the countries UK and Canada are NATO members already, and Australia and New Zealand are Major non-NATO allies.
I personally find the idea interesting, but that is about it, it would take a lot of work to make it work, and my one thing I would not want it to be is anything like the EU, we they make laws that we have to follow that don't make sense for this country.