I have been reading the Classical Field theory part from The Quantum field theory book of Lewis H Ryder. After defining classical field $\phi(x^\mu)$ he says something about adding variations on both the field, and the coordinates. $$\phi(x^{\mu}) \longrightarrow \phi(x^{\prime\mu})=\phi(x^{\mu})+\delta\phi(x^{\mu})$$ $$x^{ \mu}\longrightarrow x^{\prime \mu}=x^{ \mu}+\delta x^{ \mu} $$ Now, my question is how this $\delta x$ is different from $dx$? Clearly $\delta x$ is not just an infinitesimal number like $dx$. How does a Variation defined in such an independent variable $x$? What is exactly the definition of $variation - \delta$?
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