For those completely confused:
In the picture are the Great Muta (owner of Wrestle-1) and Jun Akiyama (owner of All Japan Pro Wrestling), shaking hands and seemingly friendly.
The Great Muta was the former owner of All Japan Pro Wrestling until he sold out to a Japanese company headed up by a major wrestling fan who wanted to compete big time with New Japan and wanted to basically be Asian Vince McMahon. Some power struggle stuff happened because Muta was still a major force in the company and after a North America tour pretty much most of the roster that Muta had built up over the years up and defected with him to found Wrestle-1. Since then Wrestle-1's been sorta there, most notable for a working agreement with Pro Wrestling Zero-1, which is a New Japan spin-off prominent for being the company of Shinya Hashimoto and featuring ex-ECW World Heavyweight Champion Masato Tanaka currently.
Jun Akiyama is a former All Japan Pro Wrestling and NOAH legend who defected to All Japan in the wake of some bad blood with NOAH along with the likes of Go Shiozaki and others, basically some of NOAH's top level guys. They breathed some life to All Japan and Akiyama found himself taking over the company's trademarks and championships. Since he's been bleeding talent, has wholesale recruited indie guys to replace said talents (mostly All Japan veterans getting traded for Osaka Pro survivors) and pretty much is dependent on BJW (a deathmatch promotion slowly turning strong-style) and their core wrestlers to stiffen up his shows.
Recently Akiyama showed up directly at a BJW for a match, indicating deeper relations than talent exchanges were possible, while this arrival indicates the possibility of Wrestle-1 talents possibly working under the All Japan banner again.
If the two living legends had any sense they'd run some unification shows and reunite their loyalists under the All Japan banner (the more prestigious, however tainted) and keep working with BJW, but they'll probably not reach the lowly heights All Japan once enjoyed in 2010, let alone 2000.