Yes, I am wrong it seems. I am unsure where I got the high<->secondary mixup from, I'm sure I saw something talking about high explosive and defining it strictly as "needs supersonic shock wave to initiate", but have just checked and can't find anything saying that. Will edit my prior comment, thanks
I'm far from an expert (I just like fun parts of youtube xD) but I'm wondering if the terms just get conflated because the only high explosives anyone will use a large amount of by choice are the stable ones, so they're (almost?) all secondaries too.