不起诉即non-prosecution。

Prosecutor/complainant not contesting the case by appearing in court nor his public prosecutor and hence his complaint is dismissed for non prosecution in court.

法定不起诉即statutory non-prosecution

绝对不起诉又称绝对不起诉，指《刑事诉讼法》第177条第1款和第175条第4款规定的不起诉。所谓法定，是指法律规定的“应当”，即是犯罪嫌疑人没有犯罪事实，或具有《刑事诉讼法》第16条规定情形之一的，人民检察院应当做出不起诉决定，检察机关不享有做出起诉决定或不起诉决定的自由裁量权，只能依法做出不起诉决定。

相对不起诉即discretionary non-prosecution

相对不起诉,又称酌定不起诉,是指人民检察院认为犯罪嫌疑人的犯罪情节轻微,依照刑法规定不需要判处刑罚或者免除刑罚的案件,可以作出不起诉决定。酌定不起诉须同时满足两个条件:犯罪人实施的行为触犯了刑律,符合犯罪构成的要件,已经构成犯罪；犯罪行为情节轻微,依照刑法规定不需要判处刑罚或者免除刑罚。

存疑不起诉即non-prosecution for insufficient evidence

存疑不起诉，又称证据不足的不起诉。存疑不起诉是检察机关对于经过补充侦查的案件，仍然认为证据不足，不符合起诉条件的，作出的不起诉决定。《人民检察院刑事诉讼规则》规定，人民检察院根据刑事诉讼法第171条第四款规定决定不起诉的，在发现新的证据，符合起诉条件的，可以提起公诉。这是检察机关对存疑不起诉案件保留公诉权的行为规范。

以下为中华人民共和国刑法中有关不起诉的相关规定，供参考：

第一百七十七条【不起诉的情形及处理】犯罪嫌疑人没有犯罪事实,或者有本法第十六条规定的情形之一的,人民检察院应当作出不起诉决定。

Article 177 Where there are no facts showing the suspects' crime or in any of the circumstances provided for in article 16 of this law, the people's procuratorate shall issue a non-prosecution decision.

对于犯罪情节轻微,依照刑法规定不需要判处刑罚或者免除刑罚的,人民检察院可以作出不起诉决定。

Where the circumstances of the crime are slight and, in accordance with the Criminal Law ,it is not necessary to give a criminal penalty or a criminal penalty may be excused, the people's procuratorate may issue a non-prosecution decision.

人民检察院决定不起诉的案件,应当同时对侦查中查封、扣押、冻结的财物解除查封、扣押、冻结。对被不起诉人需要给予行政处罚、处分或者需要没收其违法所得的,人民检察院应当提出检察意见,移送有关主管机关处理。有关主管机关应当将处理结果及时通知人民检察院。

In cases where the people's procuratorate decides not to prosecute, it shall, at the same time, release any property that it has sealed, seized or frozen. Where the person not being prosecuted needs to be given an administrative punishment and sanctions, or needs to have unlawful gains confiscated, the people's procuratorate shall submit a procruatatorial opinion and send it to be handled by the relevant organ. The relevant organ shall promptly notify the people's procuratorate of the outcome of the handling.

第一百七十八条【不起诉决定的宣布与释放被不起诉人】不起诉的决定,应当公开宣布,并且将不起诉决定书送达被不起诉人和他的所在单位。如果被不起诉人在押,应当立即释放。

Article 178 Decisions to not prosecute shall be publicly announced and the decision shall be sent to the person not being prosecuted and their workplace. If the person not being prosecuted is detained, they shall be released immediately.

第一百七十九条【公安机关对不起诉决定的异议】对于公安机关移送起诉的案件,人民检察院决定不起诉的,应当将不起诉决定书送达公安机关。公安机关认为不起诉的决定有错误的时候,可以要求复议,如果意见不被接受,可以向上一级人民检察院提请复核。

Article 179 Where the people's procuratorate decides not to prosecute a case transferred to it by a public security organ, it shall send the non-prosecution decision to the public security organ. When the public security organ feels that the decision not to prosecute was in error, it may request a reconsideration, if this opinion is not accepted, it may request a review from the people's procuratorate at the level above.

第一百八十条【被害人对不起诉决定的异议】对于有被害人的案件,决定不起诉的,人民检察院应当将不起诉决定书送达被害人。被害人如果不服,可以自收到决定书后七日以内向上一级人民检察院申诉,请求提起公诉。人民检察院应当将复查决定告知被害人。对人民检察院维持不起诉决定的,被害人可以向人民法院起诉。被害人也可以不经申诉,直接向人民法院起诉。人民法院受理案件后,人民检察院应当将有关案件材料移送人民法院。

Article 180 In cases given a non-prosecution decision where there are victims, the people's procuratorate shall send the decision to the victims. If the victims are unsatisfied, they may appeal to the people's procuratorate at the level above within 7 days of receiving the decision documents and request a prosecution be initiated. The people's procuratorate shall inform the victim of its review decision. Where the people's procuratorate maintains its decision not to prosecute, the victims may file a prosecution in the people's court. The victims may also directly file a prosecution with the people's court without having appealed. After the people's court accepts the case, the people's procuratorate shall transfer the relevant case materials to the people's court.

第一百八十一条【被不起诉人对不起诉决定的异议】对于人民检察院依照本法第一百七十七条第二款规定作出的不起诉决定,被不起诉人如果不服,可以自收到决定书后七日以内向人民检察院申诉。人民检察院应当作出复查决定,通知被不起诉的人,同时抄送公安机关。

Article 181 In cases where the people's procuratorate issues a decision not to prosecute under paragraph 2 of article 177 of this law, if the person not being prosecuted is unsatisfied, he may appeal to the people procuratorate within 7 days of receiving the decision. the people's procuratorate shall issue a review of the decision , notify the person not being prosecuted and send a copy to the public security organ at the same time.

第一百八十二条【对符合特殊条件的犯罪嫌疑人撤销案件、不起诉】犯罪嫌疑人自愿如实供述涉嫌犯罪的事实,有重大立功或者案件涉及国家重大利益的,经最高人民检察院核准,公安机关可以撤销案件,人民检察院可以作出不起诉决定,也可以对涉嫌数罪中的一项或者多项不起诉。

Article 182 Where criminal suspects voluntarily and truthfully confess the facts of the crime they are suspected of, have major meritorious contribution or the case involves major national interests, then upon approval from the Supreme People's Procuratorate, the public security organs may withdraw the case, people's procuratorates may make a non-prosecution decision, and they may also may make a non-prosecution decision for one or more of the alleged crimes.

根据前款规定不起诉或者撤销案件的,人民检察院、公安机关应当及时对查封、扣押、冻结的财物及其撃息作出处理。

Where there is decision to not prosecute or a case is withdrawn in accordance with the preceding paragraph, the people's procuratorates and public security organs shall promptly address sealed, seized and frozen assets and their fruits.