I only define soap and cream. If it's not a cream, it's a soap.
If it is consistency of Proraso green, it's a croap. Harder = soap, softer = cream. That's my standard at least.
If you can dip the brush tips to load, it's clearly a cream. Some creams dry out and require a very light loading, but you aren't building a proto-lather or anything.
Everything else is a soap, just different levels of softness. Some are harder, like Pre de Provence. Some are softer, like Cella. If you can EASILY mold it, it's a croap to me.
I only define soap and cream. If it's not a cream, it's a soap.
Okay, but . . . I have some TOBS flavors that are quite obviously creams, while others are quite a bit harder. (You scoop out a solid chunk to load your brush with in a bowl.)
It's just my own preference, but I usually call hard soaps "soaps" while soaps like Cella and Proraso are "Italian soft soaps." I suppose that makes soaps like Strop Shoppe, Maggard's, and Soap Commander "Italian-style soft soaps."
In the end, of course, we're all arguing about how many angels can dance on the head of a pin.