Let $R$ be a complete valuation ring of rank $1$ (e.g., a complete discrete valuation ring) and let $K$ be its field of fractions. Consider a proper $R$-scheme $X$ that is, say, normal (if needed). There are two ways to attach a rigid analytic space over $K$ to $X$:

- The rigid analytic space associated to the finite type $K$-scheme $X_K$;
- The rigid analytic generic fiber of the formal $\varpi$-adic completion $\hat{X}$ of $X$, where $\varpi \in R$ is some nonzero nonunit element (e.g., a uniformizer in the DVR case).

Are these two rigid analytic spaces canonically isomorphic over $K$? And if so, then why (a reference would suffice and would be much appreciated)?