My girlfriend does 3D art like this:https://jengy.carbonmade.com/projects/5522151
I think it's what she would loosely refer to as painting "baked" lighting.
Meaning its light/shadow that's a static part of the texture, and not rendered in real time.
Baking lighting can also refer to converting real time lighting into a texture.
And usually its a bit of both.
Before painting, baking on some lights can help you to identify the unwrapped parts of your model on the texture map easily.
If a texture on a model is not affected by lighting, this is commonly called "unlit", at least in Unity (Unlit shader). "Fullbright" might also be used.
I wouldn't call it unlit, because you can apply any sort of shader over the top of this.
The texture acts as a base contrast that makes the object clear under any non perfect lighting conditions.
But you're right, many games with heavy painting style textures use a shader that diplays the texture and nothing more.
And knowing that it is, we seek what it is... ~ Aristotle, Posterior Analytics, Chapter 1