Frankly I think the US and UK are calling some of the missile attacks ASBMs just to get China to think ASBMS don't work against Western navies. One of Peter Zeihan's arguments for China collapsing was he said the US was going to stop being the policeman of the world and stop patrolling international waters leaving the world's oceans open to piracy and chaos. China's economy be would grinding to a halt from all the pirates of the sea taking over Chinese cargo ships. The Western alarmists are always crying that China has a bigger navy than anyone else... Does China cause geopolitical chaos in the world? The US stops protecting the seas for its allies, no more allies' economies. That why they're there at the Red Sea in the first place.
An antiship ballistic missile is a ballistic missile capable of targeting ships. Which the munitions in question absolutely are. They may be primitive, they may be outdated, they may be ineffectual, but none of that makes them any less ballistic missiles targeting ships. A T-62 is still a tank, a T-34 is still a tank, and Little Willie is still a tank. Obsolete tanks, sure, but tanks all the same. There is nothing unusual about calling something what it is.
And the PLARF is well aware of its own capabilities relative to Iranian ones.