Variants of universal composability in security proofs
Do not take my word for it, but as far as I remember: a GUC-secure protocol is secure in the UC framework; the converse is not true since a protocol secure in the UC framework might not allow for a global setup. The JUC framework is mainly aimed toward having, in the end, a proof in the standard UC framework: a protocol secure in the JUC framework can be composed in a certain, restricted way with UC-secure protocols, and lead to a UC-secure protocol. The advantage is that JUC-secure protocols can be built more efficiently, so when this restricted composition suffices, we are fine.