The White Army was everyone that didn't like the Bolsheviks. But don't forget, it wasn't just the Red Army vs the White Army. It was also the Green Army (Ukraine), the Black Army (Ukraine Anarchists), and other factions too. Also 70,000 Japanese troops in the east, the 8,000 troops of the American Expeditionary Force Siberia in Vladivostok, the 5,000 troops of the American North Russia Expeditionary Force in Arkhangelsk, the Canadian Siberian Expeditionary Force in the northwest (troops from Canada, Australia, the UK, and some from India), the Royal Navy Squadron in the Baltics, 2,500 Italian troops, and troops from Romania, Greece, Poland, China, and Serbia. And don't forget, the Czechoslovak Legion that controlled most of the Trans-Siberian railway and all the major cities in Siberia.

All that was happening while Wrangel was staging offensives around Crimea, General Denikin from the Caucasus, General Yedenich from the northwest, and Admiral Kolchak from the Urals.
Well, at least the Black Army was useful when it staged offensives against White supply lines while the Red Army defeated Denikin's and Yudenich's armies in October and November, 1919. The Red-Black alliance was also useful in June when the Red Army drove back Kolchak in the east.

The last major Front was in Crimea where Wrangel and the last of his army was evacuated to Constantinople in November, 1920.
All that remained after that were minor skirmishes in the east that finally ended in 1934.

But what caused the divide in the Russian Social Democratic Labor Party was Lenin's views on Marxism. Lenin believed that only full-time, trained and professional Party members could effectively organize the workers. Stalin proved that he believed the same thing when he wrote his Anti-Menshevik Creed in Stockholm in 1906. Well, they were obviously right and it was also very helpful to place Tsarist soldiers in charge of the Red Army troops. By the end of the Civil War, 83% of the Red Army officers were Tsarists.

Anyway, if you want to learn more about the Revolutions and wars, Google these:

1. Vladimir Ilyich Ulyanov-Lenin.
2. Iosif Vissarionovich Stalin or Ioseb Besarionis dze Jughashvili - He was Georgian.
3. The Revolution of 1905.
4. The February Revolution.
5. The October Revolution. - Btw, the February and October Revolutions are also called the Russian Revolution.
6. The Russian Civil War.
7. World War 1.
8. The Treaty of Brest-Litovsk.
9. The Triple Entente Alliance.
10. The Communist Manifesto.
11. Leon Trotsky.

While you're reading about those, you will find tons of other cool side issues to study. Battles, alliances, and economic issues too.
Anyway, what's important about the White Army is how disorganized it was. Despite getting tons of foreign aid (mostly from fears of the effects of the Brest-Litovsk treaty), there was way too much infighting. That was also true for the Black Army. Sometimes they were fighting the Red Army but sometimes they helped them. But the Green Army was only fighting for Independence that they got in that treaty by promising to provide 1 million tons of food to Germany. It was a complicated war.
It would also be useful to read the history of Nicholas II and the Russia-Japanese war. Oh, and his German wife that was left to Rule Russia while Nicholas II played Commander-In-Chief on the front lines. She was accused of being a spy.