Salaf - literally means "those (from history) who precede, have gone before".
As-Salaf as-Saalih - The people of the past, namely the first three generations of pious muslims during and after the revelation of the Qur'an, i.e.the Sahabah (companions) of the Prophet, saaws , the Taabi'een (followers) and the Taabi Taabi'een (followers of the followers).
Islam teaches that As-Salaf as-Saalih are superior in their understanding of the Revelation of Al-Qu'ran. Generally speaking, the people present during any event (such as the revelation of the Quran) will understand it better than those who read about it later.
The Prophet, saaws, said: "I am leaving you two things and you will never go astray as long as you cling to them -- they are the Book of Allah and my Sunnah." [Reported by Al- Haakim - Sahih].
"The best of people is my generation, then those who come after them, then those who come after them (i.e. the first three generations of Muslims)." [Reported by Bukhari and Muslim- Mutawaatir. Muslim, Narrated 'Aisha - Shaykh Al Albaanee declares it Hasan in Saheeh Al Jaami' no.3288].
"The best of people are my generation, then the second, then the third, then there will come a people, having no good in them." [[related by Ibn Mas'ood] [Tabaraanee in Al-Kabeer] Shaykh Al Albaanee declares it to be Hasan. See Silsilatul Ahaadeeth ad-Da'eefah no.3569, and Saheeh Al Jaami' no. 3293.]
"My Ummah will not unite upon error." [Reported by at-Tirmidhee and Haakim - Sahih]
The best of people are my generation, then those who follow after them, then those who follow after them, then there will come after them a people who will be fat, and they will love obesity, bearing witness before being asked to."[related by the Umars, sons of Husayn(r)] [Tirmidthee, authenticated by Imaam Al Haakim] Shaykh Al Albaanee declares it to be Saheeh. See Silsilatul Ahaadeeth As-Saheehah no. 699, and Saheeh Al Jaami' no. 3294.
Salafi - means "of the salaf". The "i" (sounds like "ee") on the end of the word means "of the", "of" and/or "are". Using correct arabic grammar, the word "salafi" can only be used in association with words that are of that which is truly from the far past. In order to be a salaf, you had to exist generations prior to the current one. Referring to oneself as a salafi* is permissible in Islam so long as the intention is for identification with the salafi minhaj and this identification does not replace your identification as being MUSLIM, as this is what Allah swt has commanded us in The Qur'an to call ourselves. While it is important, as many scholars have said, to distinguish ourselves from the innovators, we first do this in our actions (i.e. do not sit with the people of innovation, engage the sunnah in our daily lives, etc.), and to do so in speech, we can best do so by clearly stating that we are followers of the pious predecessors ("Ana a-taaba as-salaf as-saalih").
Those Muslims whose intentions are to follow the Qur'an and Sunnah of the Prophet saaws and the salaf, know better than to divide themselves into a sect (a dissenting or schismatic religious body; especially one regarded as extreme or heretical) that parts from following clear proof in Quran and Sunnah.
"And this Ummah will divide into seventy-three sects all of which except one will go to Hell and they (i.e. the Saved Sect) are those who are upon what I and My Companions are upon (i.e. those who follow My Way and the Way of my Companions.)" [Reported by at-Tirmidhee - Hasan]
"Verily those before you from among the People of the Book split into seventy-two sects and verily this religion . . . ", and in another narration, " . . . this Ummah will split into seventy-three sects: seventy-two will be in the Fire and one in Paradise and that is the Jamaa'ah." [Reported by Abu Daawood - Sahih]
When questioned by his Companions about those who will be saved from the Fire, the Messenger (sallallaahu 'alaihi wasallam) replied: "They are those who are upon what I and my companions are upon." [Reported by at-Tirmidhee from Amr ibn al-Aas - classified as Hasan.]
A muslim may announce his intentions to adhere to the Dawat-us-Salafiyyah, which is identical to saying the dawah of Islam with mere emphasis on rejecting innovation in implementing and understanding the Qur'an and Sunnah of the Prophet Muhammad saaws and accepting the guidance of the Salaf-as-Saalih (as instructed by Muhammad saaws to do so). Because not one ounce of arrogance will make it into the gates of Paradise, no muslim would want to be so bold as to declare himself as a member of Firqatun-Naajiyyah (the saved group of Muslims), for only Allah swt knows who that truly is, but instead would speak of his intentions to be of the saved group, by his intentions to adhere to the dawat-us-salafiyyah.
Sheikh al-Islaam Ibn Taymiyyah said: "It is self-delusion to say 'I am saved' and not pessimistic, for example being too secure saying 'I have the attributes of the salaf, I am saved', We still have to humble ourselves and not to say that we have the attributes of the Salaf. So I say to these people, not everybody who opposes me a thing from this path will become one of those who will perish, for verily the disputer may be a mujtahid who was wrong, and Allaah will forgive him his mistakes. Or maybe the proof did not reach him, enough to satisfy his needs (i.e. to understand it). Or maybe he has enough good deeds in which Allaah will wipe away his bad deeds."
"O you who believe! Do not put (yourselves) forward before Allâh and His Messenger (SAW), and fear Allâh. Verily! Allâh is All-Hearing, All-Knowing." [Surah al-Hujuraat 49:1].
"And hold fast, all of you together, to the Rope of Allâh (i.e. this Qur'ân), and be not divided among yourselves, and remember Allâh's Favour on you, for you were enemies one to another but He joined your hearts together, so that, by His Grace, you became brethren (in Islâmic Faith), and you were on the brink of a pit of Fire, and He saved you from it. Thus Allâh makes His Ayât (proofs, evidences, verses, lessons, signs, revelations, etc.,) clear to you, that you may be guided." [Surah Al-Imrân 3:103].