You are confusing a “30 year mortgage” with a “30 year mortgage”. They sound the same, because they have the same term to repay the principal, but they are completely different because in the USA you usually know your repayments for the next 30 years, but in many other countries the repayments can go up a lot if interest rates rise.
In the USA, the usual mortgage has a fixed interest rate for the term of the mortgage. In New Zealand the interest rate is approximately a floating (edit:variable) rate over the 30 year period.
In NZ the mortgage interest rate (which controls your repayments) can be fixed for up to 5 years (the median is 2) but after the “fixed” period the interest rate resets to the current interest rates (edit: typically mortgagees lock in a new 2 year “fixed” rate at the current 2 year interest rate). NZ rates were around 2% to 3% since 2008 [1], but now they are closer to 6% [2] and most mortgage holders in New Zealand will have to pay twice as much for the interest component of their mortgage repayment, putting some people under financial stress (an acquaintance is being forced to sell an investment property because they were over-leveraged). The mortgage interest rate over the 30 year term is more of a stepwise approximation to the floating interest rate: I am unsure how much control the mortgage holder has over varying the principal repayments (I think I can pay 20% more principal per payment, shortening 30 year term to 24 years).
It is more complicated than that, and the USA has a wide variety of mortgage products you can buy including ones similar to NZ (not just the usual USA fixed rate 30 year). Other countries have their own quirks, so I am only speaking for NZ where I understand the details better.
I expect the meaning taken by the average person in different countries varies, without much overlap. My point is that mortgage products are very different in different countries, and the average person is very unfamiliar with the differences. Perhaps you are technically correct (the best kind of correct!)
For example, in Australia and NZ a “fixed rate”[1] mortgage is not the same as what you have called a “fixed rate” mortgage. Australia looks like it offers up to 10 years at a fixed rate on a 30 year mortgage (ANZ? some banks like Westpac only offer 5 years?). Banks in NZ offer up to 5 years, even though they are mostly Ozzie banks. Ozzie banks typically offer something called offset mortgages - that word doesn’t get used in NZ at all AFAIK (instead NZers can apply for a seperate revolving mortgage, I haven’t seen it bundled like in Oz).
What you call “variable rate” is called “floating rate” in New Zealand (and search completion hinted maybe the same for Canada & Singapore).
It’s even weirder in the UK because you agree a mortgage did say 30 years on a “standard variable rate” but then take a mortgage for say 5 years on a fixed rate or discounted “variable rate” which might last for 2-5 years. People do usually take a new “mortgage” after each period.
