In the 1830s, South Carolina responded to the tariff in two ways. First, they asserted that they (and other states) had the right to nullify laws made by the national government. Second, they threatened to secede from the Union. Both of these foreshadowed what they would do in 1860.
By saying that states had the right to nullify federal laws, South Carolina was essentially saying that the states were sovereign. They were saying that states could pick and choose which federal laws they would obey. This really is the next thing to saying that the states can withdraw from the Union whenever they wish. In additon, South Carolina threatened to withdraw from the Union if the federal government tried to collect the tariff by force. This is much more explicitly a movement towards secession.
Overall, South Carolina's actions in the tariff/nullification controversy foreshadowed what it would do in 1860 because it was asserting the idea that it was a sovereign state that could choose to obey or disobey the national government as it wished.