I'm reading Laurie's note about Fargues-Fontaine Curve and I think he uses a different definition of $B_{cris}$.usually when $R$ is a perfect ring of characteristic $p$, $B^{+}_{cris}(R)$ defines as $p$-adic completion of divided power envelope of the map $W(R)\to R$ and $B_{cris}=B^{+}_{cris}$.

but in these note when R is ring of valuation of an algebraically closed perfectoid field $B$ defines as completion of $frac(W(R))$ with respect to all gauss norms and defined Fargues-Fontaine Curve by it.

I want to know the relation between $B$ and $B_{cris}$ in general.is it true that they are isomorph if R is the valuation ring of a prefectoid field?