To the media, they are all "AK-47". I like to call the civilian gaggle of semi-automatic rifles "AK style" rifles. By convention, sellers call the rifles after the rifle they're patterned on, or from the donor kit, but they usually have their own model numbers.
For instance, the Hungarian AMD-65 is an AKM-based, short barrelled, select fire (selector has "safe", "auto", and "semi" settings) paratrooper assault rifle. The U.S. Army probably has a few in their museum, and if there are any legal civilian held ones in this country, it would only be a handful.
My "AMD-65" is actually a model "IAI-65". It looks like the original, but is longer barrelled to meet federal standards, and semi-auto only. Everyone still calls it an "AMD-65"
The media would call it an AK-47.
The AMD 65 is easily the ugliest variant ever produced.