There is a lot of important recent work on the construction of Calabi-Yau metrics on non-compact complex manifolds, such as $\mathbb{C}^n$. For example:

[1] Li, Y. A new complete Calabi-Yau metric on $\mathbb{C}^3$. Invent. Math. 217 (2019), no. 1, 1–34.

[2] Székelyhidi, G. Degenerations of $\mathbb{C}^n$ and Calabi-Yau metrics. Duke Math. J. 168 (2019), no. 14, 2651–2700.

Being a complete outsider, I have a very hard time understanding what exactly they mean by a Calabi-Yau metric on a non-compact manifold such as $\mathbb{C}^n$ (they don't seem to define it in their papers). For compact manifolds, one usually defines a Calabi-Yau metric to be a metric with holonomy in $\mathrm{SU}(n)$ (see, e.g., Joyce's book Riemannian holonomy groups and calibrated geometries on page 54). For simply connected manifolds, this is equivalent to a Ricci-flat Kähler metric. So is a Calabi-Yau metric on $\mathbb{C}^n$ the same as a Ricci-flat Kähler metric?

What is the definition of a Calabi-Yau metric on $\mathbb{C}^n$? Are there several equivalent definitions?