How did the abolitionist movement that arose in the 1830s differ from earlier antislavery efforts?

Actually, the two movements were quite similar in every way; the later one was simply better known because more people were literate by the 1830s.
The later movement drew much more on the religious conviction that slavery was an unparalleled sin and needed to be destroyed immediately.
Earlier opponents of slavery had called for immediate emancipation, but the later group devised a plan for gradual emancipation that won broader support.
The movement of the 1830s introduced the idea of colonizing freed slaves outside the United States, which proved immensely popular with Southern whites.