Fundamentally, the Velvet Revolution is one of the few successful modern examples of a peaceful secession, while the Prague Spring was a broad revolt against authoritarianism that ultimately was crushed with Russian Tanks. I don't think I can write all that much about the Prague Spring, but I do know a thing or two about the Velvet Revolution. And unlike the Prague Spring, the Velvet Revolution was a reaction to an unprecedented collapse of one of the power blocks that had defined global politics in the second half of the 20th century. I would can say there were three interlinked, even consecutive, forces at work in Velvet Revolution and the breakup of the Czechoslovakian state: Czechoslovakia was a country transitioning from authoritarian communism to a democratic free-market society, there were a number of divergent political currents tied to this transition, and as these differences took a regional character they were identified as the main culprit behind the country’s inability to create a new post-communist constitution.

But Czechoslovakia’s breakup was far from a foregone conclusion. At least one academic would go so far as to say it was “surrounded by a sense of evitability.” Bu although muted, historic internal divisions in Czechoslovakia were nonetheless clearly defined. At the time of secession, only three percent of residents of the Czech part of the country identified as Slovak. In the Slovak subdivision of the country, only one percent identified as Czech. Under communist rule, there had been separate Czech and Slovak communist parties as well as ethnically separate parties of the token opposition. In addition, national politics tended to be in the purview of a political class largely hailing from Czech lands, while save for a few prominent examples, Slovak politicians seldom made the jump from regional to national politics. After 1989, the post-communist political order retained these qualities.

Initially, these ethnic divisions did not pose significant barriers to forming governing coalitions. As in all pluralistic parliamentary democracies, compromise and coalition building was accepted as an integral part of government. However, after the 1992 election it became clear that Czechs and Slovaks were very divided in their political preferences: The Czechs favored the Civic Democratic Party, whose platform was geared towards rapid economic reform; on the other hand the Slovak voting bloc favored the Movement for Democratic Slovakia, which was not only ambivalent to economic reform, but also driven by platform with markedly nationalist undertones. Both parties neatly split the federal parliament, with large leads over their closest rivals.

The situation was thus poised for moderate socio-political electoral divisions to mutate and take on a self-reinforcing ethnic character: Czechs preferred politicians promising rapid reforms, while the Slovaks were more cautious. Conservativism was also entrenched through a religious dimension: The Czechs were ambivalent about religion, while the Slovaks had held onto their catholic beliefs in spite of decades of communist secularization. This kind of divide is typical of urban and rural voters in other countries, and indeed the Czech Republic was more urban than Slovakia.

Perhaps as a consequence of geography, Slovaks were also more prone to look eastwards in international matters. Although both Czechs and Slovaks looked very favorably upon admission to growing pan-European institutions like the ECC, Slovakia’s eastern neighbors remained its most important export market. This too would reveal itself to be a source of tension, as in April of 1991 the very popular Slovak Prime Minister Vladimír Mečiar was forcibly removed by the government in Prague following, among other things, allegations he had approved a clandestine arms sale to the Soviet Union.

With the existence of three parliaments; the Bicameral Federal Assembly and the separate Czech and Slovak national councils, the legislative system in Czechoslovakia was a gridlock waiting to happen the instant political differences took a geographic character. The division of legislative and administrative responsibilities were never clearly defined under Communist Party rule, and after 1989 the legislative system found itself ill-suited to the task of creating a new constitution suitable for post-communist society. By 1992, the only thing Czech and Slovak legislators could agree on was to separate the country. Thus began the “Velvet Divorce;” so called because of its seamless and peaceful implementation.

If you're interested in the Prague Spring, which I didn't really touch upon, I'd suggest the seventh chapter of Mark Gilber's Cold War Europe, which is probably one of the most comprihensive histories of modern Europe out there. The full citation is: Gilbert, Mark, Cold War Europe: The Politics of a Contested Continent, Rowman & Littlefield (Lanham MD), 2014

For the Velvet Revolution, you can read about both the Czech and Slovak sides respectively here:

Balík, Stanislav, et al. Czech Politics: from the West to East and Back Again, Barbara Budrich (Leverkusen DE) 2017

Kirschbaum, Stanislav J. A History of Slovakia: The Struggle for Survival (II ed). Macmillan (New York NY) 2005

And a comprehensive examination of the "Divorce" itself here:

Henderson, Karen. “Czechoslovakia: The Failure of Consensus Politics and the Breakup of the Federation.” Regional & Federal Studies, vol. 5, no. 2, 1995