This is a question I have been asking myself for years. One theory that I've often had, is that Character Product/Charapro is a sister company of Bandai.
Bandai's Toukon Battle Royale Masahiro Chono from 1996 looks a lot similar to Toukon Shop/Charapro's New Japan Superstars straps from 1997.
Bandai had a working relationship with NJPW for years - going back to 1981 with the original Popy figures (Popy being a sister company of
Bandai).
Bandai's involvement continued into 1986 with "The Pro-Wrestler" line of keshi. Rumoured to be created in small quantities, Bandai's Pro-Wrestler line is
considered the rarest Wrestling eraser series (outside a small group of M.U.S.C.L.E. figures) with certain Wrestlers selling for hundreds of dollars a piece!
Charapro also released Mini Big Head figures for Kinnikuman. The Mini Big Head moniker was additionally used for Dragon Ball Z
figures. However, these figures were released under Bandai's Popy line. Confusing.
Before the launch of Toukon Shop's Hyper Heroes line in 1997, Banpresto (another subsidary of Bandai) released
their own realistic Wrestling figures in 1996 with the 'real figures in Tokyo Dome' gatchapon set.
While the figures contained realistic proportions (a rarity in Wrestling figures in general), I wouldn't consider them
action figures. More so with their smaller scale as buildable model kits/gumball machine prizes (better known as
Gatchapon in Japan).
As for Character Product and Mogura House, I say it all came down to licensing and location. Mogura House, if I recall,
was in the same factory location as Character Product. Just the same as IMA Corp (who handled keychain figures for
K-1) was relatively close by, too.
Generally, Toukon Shop was the NJPW official merch store of the same name. So, any figure series featuring NJPW at
the time was primarily released under the Toukon Shop banner (with some exceptions). Charapro was known for
handling licenses outside of NJPW such as AJPW, RINGS, PANCRASE, K-1 and Michinoku among others.
It seems Mogura House specialized in licensing Pro-Wrestling NOAH along with special cases such as Rikidozan and
Hayabusa (who was forced to retire, just as Charapro and Mogura House began producing figures on their own).
Why so many different company names for the same manufacturer? I assume it's a Japanese law policy that I am not
familiar with. Maybe certain Wrestling promotions didn't want to be associated with one another - thus, the name
change.