As an American growing up in the late 70s/early 80s, we called all die-cast metal cars “matchbox cars,” even though many (all?) of them were Hot Wheels. I never knew there were two competing brands.
Growing up in the 1960s we called them all Dinky Toys. Dinky was the best: they even had die-cast UFO SHADO interceptors and Space:1999 Eagles in the 1970s when I was too old for such things (but still secretly coveted them).