Yes, that was the first war if I am not mistaken. Then in the second war, since SW got their butts kicked in the first war, they fled to lordaeron and that is when the alliance of lordaeron was formed, uniting the humans like gilneas, KT, SW, as well as gnomer, IF, and quelthalas (but the prince wasnt super motivated until maybe later I think). I have been piecing what I can together from wowpedia to better understand, so unless that source is just flat out wrong that is my current understanding of events.
Heres some snippets from what I have gathered on wowpedia.
Troll Wars
“The Troll Wars were a series of conflicts between the forest trolls of the Amani Empire and an alliance of the humans of Arathor and high elves of Quel’Thalas, ending approximately 2,800 years before the coming of the orcs to Azeroth.[6]”
"Chieftain Thoradin of the Arathi saw the threat to his race and decided to unite the humans. Along with his trusted friend and greatest general Ignaeus, later to be known as Trollbane, he devised a cunning strategy: fight the nearby human tribes, and after each victory offer them peace and equality. With this tactic, he united the tribes and founded the first of the human kingdoms, Arathor. Situated in what is now known as the Hillsbrad Foothills and Arathi Highlands, his growing empire ruled from the capital city of Strom. Up to this time, the human empire had rarely had contact with the reclusive, magic-wielding elves, and all contact with the trolls was through border skirmishes.
After years of continual besiegement by the trolls, the high elves, with defeat nearing, finally decided to seek the aid of the now-powerful humans of Arathor. The elven king Anasterian Sunstrider, a descendant of Dath’Remar, sent out their diplomats to try and negotiate the primitive humans into aiding them. Even though the elves had at times treated the humans no better than they had the trolls, Thoradin saw the danger in allowing the elf civilization to fall, and agreed to an alliance. The elves would teach one hundred humans how to wield the arcane arts of magic, while the massive armies of Strom would mobilize and join the war against the trolls.[11]"
Arathor
Following the defeat of the trolls, the human mages that had been instructed by the high elves eventually chose to leave Strom and found their own nation, Dalaran, dedicated to the study and use of magic. In time, other city-states were founded: Gilneas, Alterac, and Kul Tiras. Much of the nobility decided to move from Strom to the fertile lands of the north, founding Lordaeron, while the heirs of King Thoradin traveled far south to form the kingdom of Stormwind. The few remaining loyal defenders of Strom renamed it Stromgarde thus creating the Kingdom of Stromgarde, a shell of what was left of a once-great empire.[8]
Anduin Lothar
“Sir Anduin Lothar, the Lion of Stormwind, was the last true descendant of the ancient Arathi bloodline, a Knight Champion of the Kingdom of Stormwind during the First War,[7] and the Supreme Commander of the armies of the Alliance of Lordaeron during the Second War. He perished in combat at the base of Blackrock Mountain just before the end of the Second War and the closing of the Dark Portal. He is considered one of the greatest warriors in human history.[8] King Varian Wrynn named his son, the current King of Stormwind, after him.”
First War
“The First War (also referred to as the first Great War)[45] was a conflict fought between the orcish clans of Draenor and the humans of the Kingdom of Stormwind.[7]”
“Anduin Lothar had no other choice than to declare the war lost[91] and save what remained by gathering the tattered remnants of the army and as many civilians as he could to lead them in a desperate retreat across the Great Sea, toward the northern kingdom of Lordaeron to beseech aid from King Terenas Menethil II.[92”
Second War
“The Second War, also known as the second Great War,[6] was a major conflict that took place in the Eastern Kingdoms around four years following the opening of the Dark Portal,[7] between the armies of the Orcish Horde and an Alliance of several other races. The conflict immediately succeeded the First War and saw the two factions clash for mastery of the entire continent, as well as Azeroth at large.”
“As the Horde further marshaled its strength in the south, the Council of Seven Nations continued in Lordaeron’s Capital City. Those in attendance still found themselves debating a proper response to the orcish threat, as well as the merits of human unity. In attendance were all major rulers of Azeroth’s human nations, including: King Terenas Menethil II of Lordaeron, King Genn Greymane of Gilneas, Lord Admiral Daelin Proudmoore of Kul Tiras, King Aiden Perenolde of Alterac, Archmage Antonidas of Dalaran, and King Thoras Trollbane of Stromgarde. Also present was Sir Anduin Lothar, representing the recently-ruined Kingdom of Stormwind.”
Aliance of Lordaeron
"The Alliance of Lordaeron (aka Lordaeron Alliance,[1] Great Alliance,[2] Grand Alliance,[3] Human Alliance,[4] or Alliance[5]) was the union of the seven human kingdoms, along with the dwarves of Khaz Modan (which also included the gnomes of Gnomeregan) and Aerie Peak, the high elves of Quel’Thalas, and others with major political influence including the Church of the Holy Light.
Following the destruction of the Kingdom of Stormwind by the Orcish Horde, its survivors fled to Lordaeron. Realizing the threat the orcs posed, Regent Lord Anduin Lothar, leader of Azeroth’s refugees, was able to convince the leaders of the other human kingdoms to join against the orcs. The Wildhammer dwarves of Aerie Peak and high elves also soon joined the Alliance, as well as the gnomes of Gnomeregan and the Ironforge dwarves later in the war."
"Quel’Thalas, the kingdom of the high elves, is located on the northern tip of the continent of Lordaeron, northeast of Stratholme. At the time of the Horde’s approaching invasion of Lordaeron, King Terenas sent emissaries to High King Anasterian Sunstrider and the Convocation of Silvermoon. In it, Terenas mentioned that Lord Lothar was the last descendant of King Thoradin of Arathor. Millennia earlier, during the Troll Wars, the elves had made a pact to aid Thoradin and his descendants, the Arathi. Anasterian, seeking an opportunity to fulfill the Sunstrider dynasty’s debt to Thoradin, grudgingly sent a small force to the Alliance armies stationed in Hillsbrad. The party was led by Alleria Windrunner, a captain in the Silvermoon Ranger Corps.
When the Horde invaded Quel’Thalas and began burning the edges of Eversong Forest, Alleria returned to Silvermoon City to warn of the oncoming Horde and when Anasterian and the Convocation refused to acknowledge the threat, Alleria threw the head of a forest troll at Anasterian’s feet, saying that she and her sister Vereesa had slain the troll near a river not far from Silvermoon. This provoked a reaction from the high king, who had fought against the trolls during the great war millennia earlier, and he ordered the full mobilization of his army to combat the Horde onslaught.
After the Second War, tensions began to arise between the high elven nation and its human allies - humanity came to distance itself from Quel’Thalas; the elven kingdom in turn proving to be an uneasy ally.[18] The tension came to a a head when High King Anasterian Sunstrider seceded - the catalyst that led to both Gilneas and Stromgarde following suit; a turn of events that changed the face of the Alliance and weakened it considerably.[19]"
That’s everything I have pieced together that is as concise as I can get it, but shows the summary of the history. All from WoWpedia with the titles of the articles italicized.