-Certificate of Eligibility For a Status of Residence (在留資格認定証明書)
If a foreigner has this certificate before entrance into Japan beforehand, the period of issuance of a visa can be shortened.
-Permission to Acquire Status of Residence(在留資格取得許可)
This is related to a foreign national who is to stay in Japan without getting through the procedures for landing (e.g.,in case of birth in Japan, renouncement or loss of Japanese nationality).
-Re-entry Permission(再入国許可)
If you leave Japan without obtaining a re-entry permission beforehand, it is necessary to obtain a visa newly. Therefore it takes more time. Then, this is permission for re-entering quickly.
-Alien Registration(外国人登録)
All foreign nationals residing in Japan are required to register at the municipal office of the city, ward, town or village, in which they are living. This must be done within a certain amount of time from the day of their arrival in Japan.
-Permission to Change Status of Residence (在留資格変更許可)
It is related when a foreigner desires to cease his present activity and is going to concentrate on an altogether new activity which falls outside those permitted by his Status of Residence.
-Permission to Extend Period of Stay(在留期間更新許可)
If a foreign national desires to remain in Japan under the same status of residence beyond his authorized period of stay,it is necessary to apply for and obtain an extension of period of stay.
-Permission to Engage in an Activity Other Than That Permitted by the Status of Residence Previously Granted (資格外活動許可)
For example, it is related when a pastor is going to teach a foreign language in a linguistic school.
-Permission for Permanent Residence(永住許可)
Permanent residence is permitted only when a foreign national has established a permanent base of livelihood and when it is deemed that his permanent residence will be in accord with the interests of Japan.
The above are some examples.
For more information,please ask experts.
CF: http://www.atlo.jp/entop.html
http://www.hire.jp/01.html