1.Types of Entities

There are lots of types of corporation under Japan Law, which are categorized by Companies Act and other laws.
The first category, based on Companies Act has 4 types, called Kabushiki Kaisha(Stock Company), Goudou Kaisha(Limited Liability Company), Goushi Kaisha(Limited Partnership Company) and Goumei Kaisha(Partnership Company). Kabushiki Kaisha(Stock Company) and Goudou Kaisha(Limited Liability Company) are limited liability entities. Goushi Kaisha(Limited Partnership Company) and Goumei Kaisha(Partnership Company) are partially or entirely unlimited liability entities.
Therefore, the formers are popular and especially Kabushiki Kaisha(Stock Company) is well known to not only Japanese people also some other people.
Meanwhile, other types of corporation are established in many sorts of laws, categorized by purpose, governance, special requirement and so on. Examples of them are Non-Profit Organization, Ippanshadan Houjin(General Incorporated Association), Ippan Zaidan Houjin(General Incorporated Foundation), Syukyou Houjin(Riligious Corporation).

2.Kabusiki Kaisha

As already mentioned, Kabushiki Kaisha(Stock Company) is most popular and familiar to people not only here also overseas.
The Companies Act
was adopted in 2009 instead of abolishing a part of the Commercial Cord. Since the time, setting up Yugen Kaisha newly has been prohibited, which has good points for small businesses. Now, there are roughly 2 types of Kabushiki Kaisha(Stock Company). One is with Board of Directors, which is a traditional style. This type is mainly for big companies including listed companies which must have this system. This requires at least 3 directors (1 representative director in them) and 1 statutory auditor. The other is without Board of Directors which is a new style. This requires at least only 1 (representative) director.
In Japan, basically almost any nationality can own 100% share of a company. Therefore, foreign company can have 100% subsidiary company. Besides that, foreign nationality can be either a director or a representative director. Minimum capital amount was abolished and you can put only 1 JPY as a capital amount. However, if you would apply for the “Investor/Manager” visa, 5 Mil JPY as a capital amount should be recommended.

3.Difference between Kabusiki Kaisha and Goudou Kaisha

In mergers and acquisitions, there are mainly 5 types of way or their combination, which are Merger, Assignment of Business, Company Split, Share Exchange and Share Transfer.

Merger means

Companies Act
Article 2
(xxvii)　"Absorption-type Merger"　means any merger Company(s) effects with another Company(s) whereby the surviving Company succeeds to any and all rights and obligations of the absorbed Company(s);
(xxviii)　"Consolidation-type Merger"　means any merger effected by two or more Companies whereby the new Company incorporated by the merger succeeds to any and all rights and obligations of the companies consolidated by the merger;

quoted by http://www.japaneselawtranslation.go.jp/

In other words, a merger company or a new company set up by the merger succeeds to all assets and liabilities.

Assignment of business is, on the other hand, in assignment of business, a portion of or the whole business is transferred from one company to another company by the way each asset is specified. Main differences between merger and assignment of business are about applied tax regulation, dept (liability), procedure regarding approval from government and so on.

Company Split means

Companies Act
Article 2
(xxix)　"Absorption-type Company Split"　means any Company split whereby succeeding Company(s) succeeds after the Company Split, in whole or in part, to any rights and obligations, in whole or in part, in connection with the business of the Stock Company(s) or the Limited Liability Company(s) which is split;
(xxx)　"Incorporation-type Company Split"　means any Company split whereby new Company(s) incorporated by the Company Split succeeds to any rights and obligations, in whole or in part, in connection with business of the Stock Company(s) or the Limited Liability Company(s) which is split;

quoted by http://www.japaneselawtranslation.go.jp/

From the point of the legal view, this is similar to merger rather than assignment of business because of “succeed to all assets and liabilities”.

Share Exchange Means

Companies Act
Article 2
(xxxi)　"Share Exchange"　means any exchange of shares whereby Stock Company(s) cause all of its issued shares (hereinafter referring to the shares issued by a Stock Company) to be acquired by another Stock Company or Limited Liability Company;

quoted by http://www.japaneselawtranslation.go.jp/

and share transfer mean

Companies Act
Article 2
(xxxii)　"Share Transfer"　means any transfer whereby Stock Company(s) cause all of its issued shares to be acquired by a newly incorporated Stock Company;

quoted by http://www.japaneselawtranslation.go.jp/

Both are mainly for making a holding company and the group companies. The former is for like company to become a holding company already exists and the latter is like company to become a holding company is newly set up.