This is a question I have fielded quite a bit over the years. I still have trouble finding a label for what I do... maybe because I don't like labels. When people ask what I am or do. I usually just say I am an artist. Sometimes I say I am a toy maker, but then almost immediately regret it, as that can feel and sound so limiting. So I say I am an artist. If the person asking asks what kind of artist, well that depends on the day and mood, but often I follow up with "I am a painter" or "I make toys for big people".
I'll try to define a few of these toy labels here.
Art Toy. I think of this as EVERYTHING. if you make art, and it's a 3-D object that you can play with, then it's an ART TOY. It has a Sorta "Western artist" label attached to it, which means an artist from anywhere but Asia.
Kaiju. This I think should only be applied to toys that are directly inspired by the Japanese monsters of yesteryear. You love Godzilla and Ultraman, then yes. You have a toy that was greatly inspired by the Hulk, probably not. Is Booska (whick just looks like a really cute deformed chipmunk) a Kaiju. Most Definitely yes. What about a Funko Pop toy of Scooby Doo? No. It has a lot to do with the esthetics and link to these vintage Japanese monsters. Really maybe August Ragone should be answering this one though. It gets so gray and muddy.
Sofubi. This one can easily get muddy too, but the best answer is anything made in JAPAN out of soft vinyl. Lately there are a lot of toys made out of nearly the same formula in china. I don't see anything wrong with this this, I just wouldn't call it Sofubi. Maybe it's an art toy or even kaiju. Again, this is mostly esthetics. In Japan these are made by craftsman, always.
Soft vinyl. This I understand is a form of PVC, please correct me if I am wrong. Soft vinyl is made using sometimes rotocasting techniques, and always is slush cast. The maker can control how squishy it is by changing the formula, or simply making the walls of the vinyl thicker. I'll go further into this, with future FAQ answers.
Hope all this helps a little.