I don't consider the Chavez project a /revolutiojnary/ International. It's too broad and all over the map. It's been proposed to include parties like the PRD in Mexico and other populist and centrist formations. I'm very skeptical about the so-called Fifth International. The PSUV itself includes native bourgeoisie allied with Chavez. It's a popular front/multi class party. I'm also concerned that the PSUV sent a delegation of 100 leaders for "ideological training" in China by the CCP. Not a good sign.
Insofar as how you define /revolutionary/ when discussing International projects, I guess any International formation that promotes a transition to socialism might meet the requirements of the Feds. Becoming the "official" section is prohibited by law. Any group that wants to affiliate to the FI or any other International is constrained by law. Hence, "sympathizing" status. As far as I know both the FIC and SA are sympathizing organizations. The ISO is an "observer."
I'm no legal expert - just a construction worker. I also don't quite get the practice of having two or more "sections" in one country. The practicce is such that when a section splits, the FI tries relate as best it can to both sides of the split. I think the reality is that they encourage cooperation and eventual reunification, but sometimes positions and practices prohibit such. In Gernamy for instance the section is split in two. They cooperate to publish INPREKOR but take very different approaches to Die Linke - one inside as a tendency and the other outside.
In the US the differences between Solidarity and SA are sometimes harder to quantify. One is on electoral politics. Solidarity supports Green and non-socialist candidates, as do the CWI and IMT sections. SA has a policy of only supporting canidates that are /clearly/ socialist and independnet of the two bourgeois parties.
SA has a policy aimed at "party building" and developing a programmatic approach to struggles. Solidarity, it seems to me, (based on 16 years as a member) does little to educate its younger members and to build itself. Especially in labor work, where they do some good things, they separate their socialist politics from their mass politics.