I’m guessing by Alids they are referring to all of the original backers of Ali, whereas when they say Shi’a they are referring to just that subsection that stuck with that support. But I’d have to see the context. In the meantime, perhaps this will help, an old post now heading for its record third thread ( stock answers? yes, we have those ) :
Okay, for those few who may be interested, once again I present Tamerlane’s Thumbnail Sketch of the Origins and Early Development of Shi’ism ( originally posted way back in the first “Ask the Muslim Guy” thread ) :
Although I think this has already been covered in part, I’ll take a stab at the question of the Shi’a/Sunni split. It was not really a doctrinaire religious split like the Catholic/Protestant rift, nor was it really a geographic split ( though there were very limited elements of that ). Rather, despite some definite religious overtones from the beginning, it was primarily a political fissure.
The central issue was the succession to Muhammed. Muhammed was none to clear on just what was to happen after he died in 632 C.E. ( in part it may be that death crept up on him sooner than he expected ). There are some ( disputed by Sunni scholars ) indications that he favored his family, personified in his son-in-law and cousin, Ali ( who was also the first male convert to Islam, though not the first male adult convert ). It seems pretty clear that Ali himself was of this opinion. However Ali was a polarizing figure with limited backing and the Islamic state was in a fragile position. In particular the situation in Mecca, just recently converted, was unstable, but it was there that the bulk of the Islamic state’s resources were concentrated ( to oversimplify vastly, Ali drew his support more from Medina, his opponents from Mecca ). Some of Muhammed’s most important Companions, led by Umar, seized the bull by the reins and quickly convened a council and had Abu Bakr, an extremely clever man and skilled politician with strong support from the all-important Quraysh tribe of Mecca, elected to the post of Caliph. The explanation given was that this was a traditional Arab way of deciding the succession of a community ( Sunnah=tradition, hence "Sunni ). This was then presented as a fait accompli to Ali, who was caught by surprise and NOT happy about it. After some resistance he acquiesced with poor grace. This began the split.
After Abu Bakr died, Umar engineered his own election and sought some rapproachement with the disgruntled Ali, with some, but not complete success. After Umar was killed by a slave, Uthman of the Banu Umayya beat out Ali ( still with only limited support ) in a further election. However his twelve-year reign proved tempestuous and was marred by a certain dictatorial bent and rampant nepotism. He also ( in contrast to Umar ) pursued a policy of centralization. All of this stirred tremendous resistance and led to armed rebellions. One of these rebel parties, proceeding from Egypt, murdered Uthman in Medina in 656. The various rebel factions that now dominated Medina proceeded to place their backing behind Ali, who though he had argued against violence, was tainted by being supported by Uthman’s murderers. Further though he considered himself Caliph by legitimate descent, he was not elected by a Shura ( council of senior Muslim leaders ) as Umar had stipulated should be done and lacked the backing of the Quraysh, which Abu Bakr had proclaimed as the ruling class in Muslim society. He was thus immediately challenged by Mu’awiya, the powerful governor of Syria and Uthman’s closing living relative.
This triggered the first ( of four ) fitna , or Islamic civil wars. At first Ali was successful, winning an advantage at the battle of Siffin. But he then made a horrible political blunder by agreeing to an arbitration with his opponents that made significant concessions. Since he had been waging this war as a struggle against un-Islamic rebels that had earlier been declared unfit to hold office, this arbitration was considered heretical backsliding by a minority of the heterogenous factions that made up the early Shi’a movement. One group ( who were largely desert Bedouin with definite anti-centralizing and egalitarian tendencies ) seceded and declared a general war on both Ali and Mu’awiya - These became the Kharijites.
The Kharijites considered their allegiance to not be bound to a particular person, but rather to Qur’an and the Sunna of Abu Bakr and Umar ( they conveniently overlooked or ignored those two Caliph’s elevation of the Quraysh, to which they were fiercely opposed ). They were critical of Ali’s claim to the Caliphate based on his early merits and kinship with Muhammed. In their eyes early merit could ( and in this case was ) be lost by an infraction of divine law ( as they considered Uthman and Mu’awiya to have lost it ) and kinship with the Prophet was irrelevant.
Weakened by the aftermath of the arbitration at Siffin, Ali’s position eroded as he now faced a multi-front struggle. In 661 he was assainated by Kharijites and his son and successor al-Hasan surrendered to Mu’awiya who inaugurated the Umayyad dynasty.
At this point Shi’ism was still more a political force, but it was beginning to gather religious differentiation. Ali’s second son, al-Husayn, died in an abortive revolt attempt at Karbala in 680 and became a martyr to the Shi’ite cause. A son of the fourth Imam, Zayd, died in a rebellion against the Umayyads, causing his followers to split off as the militant Zaydi Shi’ites ( “fivers” ), who only recognized the first four Imams, plus Zayd ( a non-designated son ) as legitimate - To the Zaydi’s, designation of successors ( accepted by other Shi’ite factions ) was unimportant, it was only those that struggled against oppressors that were worthy of the Imamate. The Zaydi’s today dominate northern Yemen.
By the 740’s resistance to the Umayyads, who were extremely Arabo-centric and plagued by some poor rulers ( only Umar II is uniformly praised by Sunni biographers ), began to intensify. The Abbasids, a family that was descended from the Prophet’s uncle, Abbas, began to gather steam in Khurasan in the east, drawing particular support from some Shi’ites and the mawali ( Persian converts to Islam slighted by Umayyad policy ). After being badly weakened by a serious of disastrous military defeats ( to the Khazars, the Byzantines, and North African Kharijites ) and a fratricidal succesion struggle, the Umayyads were swept from power by the Abbasids in 749.
This occasioned a further split in the Shi’ite community. Those that were content that members of the Banu Hashim ( Muhammed’s family, essentially ) were now in power, in the form of the Abbasids, merged into the Sunni mainstream. Those that contended that only Ali’s direct descendants should rule, remained as Shi’ites. From this point, that definition of Shi’ism became codified.
The true development of Shi’ism as an entirely different religious sect, with significant differences in jurisprudence and doctrine from mainstream Sunnism, solidified under the sixth designated Imam ( in direct descent from Ali ), Ja’far al-Sadiq ( who worked under the protection of the Abbasid Caliphs ). From this point forward, though there were many elaborations and one further split after Ja’far’s death into the Isma’ili/Sevener and Imami/Twelver sects ( the Imami’s are the “mainstream” sect that one finds in Iran, southern Lebanon, and southern Iraq today ), one can consider Sunnism and Shi’ism as different religious movements in the fullest sense.
For a good analysis of the reign of the first four Caliphs ( the Rashidun, or “Rightly Guided Caliphs” ) and the first fitna, I’d recommend The Succession to Muhammed:* A Study of the Early Caliphate* by Wilferd Madelung ( 1997, Cambridge University Press ). Note that in terms of Muhammed’s wishes, his own analysis comes down in favor of the Shi’ite interpretation - But that is not necessarily a consensus view.
addendum ( originally a second post, eited to exclude details on the Ismai’ili/Imami split ):
Less I was unclear, the fourth Imam, the son of al-Husayn, wasn’t named Zayd ( it was Ali Zayn al-'Abidin ), rather that was his son’s name. The fourth Imam’s designated heir, who is accepted by both Isma’ili and Imami Shi’ites as the legitimate fifth Imam, was Muhammed al-Baqir. He predeceased his younger brother Zayd in 731. So at the time Zayd died a martyr in 740 and the Zaydi split happened, the other Shi’a factions were already under the authority of their sixth Imam, Ja’far al-Sadiq ( who died in 765 ), whose authority the Zaydis rejected. Hope that’s not too confusing.
I should note that from Ja’far al-Sadiq through Hasan al-'Askari, all of the Twelver Imams lived under the protection and patronage of the Abbasid court, where they were treated with honor as Holy Men and had considerable influence in merchant and scribal circles. This goes a long way to explaining the relative passivity and apolitical bent of the early Imamis, as opposed to the militant Zaydis and Isma’ilis.