Is there a difference between natural and organic?

Yes, organic is a specific method of growing produce that is free of pesticides and chemicals. Just because something is not organic does not make it un-natural.

I do not give advice for products/formulations intended for animal use e.g dog shampoo. If I have not tested something on myself then I cannot answer your question.

Labelling your products: List all inci names. Standard protocol of warnings should apply e.g. if you should experience some irritation, discontinue use immediately.