I think the semantics of it are open to interpretation, but it really depends on the context you're using it in. If I were to describe a texture that looked as though it was literally painted in real life, I would say that you could see the brushstrokes or there was primer underneath the coat of paint. If I were to hear…
When you say 'hand painted textures' do you mean making the texture map look as though someone has literally 'painted' it, or do you mean using something like a Wacom tablet in Photoshop? Most texturing guides/tutorials are going to assume that you are 'painting' your texture maps. It is very rare (and very limiting) if…