Understanding BlackJax's Implementation of MEADS

[giladturok]

The BlackJax documentation for MEADS here states that

This is an implementation of Algorithm 3 of [HS22] using cross-chain adaptation instead of parallel ensample chain adaptation.

What does cross-chain adaptation instead of parallel ensemble chain adaptation mean and what are its implications?

I read the original MEADS paper and previous BlackJax Github issues/pull requests, but neither helped. Thanks!