From that website, "Turface MVP" is an expanded rock that absorbs water into each grain, but is coarse enough to allow air flow around the grains.
#2 Chicken Grit is coarse enough for most of my purposes, but I don't grow cacti. I would think that turkey grit would be plenty large for most horticultural uses.
I agree that anything called "sand", even "coarse sand" is actually going to be entirely or mostly much too fine.
If you can find a place that sells to people who mess with concrete, look for different grades of "crushed rock" or "crushed stone". If it isn't hugely expensive, it may include some fine stuff that you will have to screen out or blow away or put up with.
I think you probably want grain sizes around 2-3 mm. Around 1/10 inch. Like, between 1/16th inch and 1/8th inch. Grit much smaller than 1 mm probably increases water retention, instead of decreasing it.
But once again: I don't grow cacti. I'm just aiming for very fast-draining potting soil.