I have tried to find this out through google and searching this site with no luck. Basically, are the terms 'law' and 'identity' interchangeable in Mathematics? What is described as 'logarithmic identities' in one place is referred to as 'log laws' elsewhere. Similiarly, 'index laws' and 'exponential identities'.
In trigonometry, there are identities such as $\cos^2(x)+\sin^2(x)=1$ and $\sin(2x)=2\sin(x)\cos(x)$. But then there are "laws" such as $c^2=a^2+b^2-2ab\cos(c)$. The law of sines and law of cosines are not identities because they are true only for triangles in the Euclidean plane. There are different but analogous laws for triangles in the hyperbolic and elliptic plane.
So in trigonometry there is a distinction between an identity and a law.