Was there a difference in this period from identifying as an abolitionist and being anti-slavery?
Yes! Yes! Yes! Just gave a lecture on this to my US History undergraduates.
Abolitionists generally based their opposition to slavery on moral reasoning based on the inhumane treatment of the slaves, the degrading effect it had on whites (Northern and Southern), and its contradictions with notions of American freedom. There were, of course, different flavors of abolitionism, the most radical and moralizing being people like William Lloyd Garrison who refused any kind of moral compromise on the subject. Others were more willing to work within the system and compromise on the moralizing rhetoric if it meant more votes. That pro-compromise group usually held the most sway in organizing the abolitionist political wing, the Liberty Party.
That said, the Liberty Party was a freaking joke. There were around 100,000 abolitionists in the US around 1840 (which is a pretty tiny fraction of the North despite looking like a big number), but the Liberty Party got a whopping 7,000 votes in the presidential election. The Party worked hard on its image and engaged in a lot more compromise to try and draw in anyone who opposed slavery for any reason. All this work, in 1844, got the Liberty Party a whopping 62,000 votes or 2.3% of the electorate, just enough to pull a Ralph Nader and keep Whig candidate Henry Clay from winning the election. That's the peak of abolitionist political success. Moral of the story: abolitionism is never ever especially popular in the North.
Being antislavery is COMPLETELY different, and something a lot more Northerners are ultimately willing to get behind. Antislavery positions usually involved opposing slavery for reasons other than morality and humanity. One of the early instances of this comes up during the congressional gag-rule on abolitionist petitions between 1836-44. Abolitionists had been submitting petition after petition to Congress opposing slavery (they were persistent as they were annoying), and it got to the point of a media spectacle due to the way proslavery congressmen were suppressing their entrance into congressional debate of any kind. Ultimately, Northerners started to wonder why upholding slavery seemed to trump the rights of white Americans in the North to legitimately petition their government for a redress of grievances. Most Northerners didn't give too much of a shit about the welfare of black Americans but they did care about their own rights. Gag rule eventually gets repealed.
This happened in other cases as well. Fugitive slaves: We don't have or want slavery here, and so why should we be forced to help Southerners enslave people? Why must we protect their sovereign state rights when supporting slavery, but they don't support our sovereign state right to enact personal liberty laws? What if I don't want to be forced into a posse to help a slave catcher? (Prigg v. Pennsylvania, Fugitive Slave Law of 1850, eventually Dred Scott).
The West is a huge one, and deals with economic rights more than political ones. Northerners view the West as key to their economic future. It provides cheap land and opportunity for Northerners to make their own fortune and secure independence for themselves. But that gets taken away when a slaveowner can stroll in with 20 slaves. Joe Northerner can't compete with that, and non-extension of slavery becomes a huge issue for North. See the Mexican War and Wilmot Proviso, the Kansas-Nebraska Act, and Bleeding Kansas.
Connected to this is free labor ideology, which becomes a powerful economic vision for Northerners in the mid-1840s and beyond. Free labor ideology stresses the virtue of hard work and personal independence through the acquisition of land, a business, etc. Working for someone else, unless its a temporary position on the way to true independence, becomes absolutely abhorrent to Northern mindsets with the rise of free labor ideology. And slavery spits in the face of it all. Black Americans are denied the right to their own labor and white Southerners get rich by unfairly exploiting someone else's labor rather than working for it themselves. If slavery expands, Northern opportunity declines. Antislavery politics is a direct result of this realization.
In short, antislavery positions are usually born out of some form of self interest, protecting the political and economic rights of white Northerners while the welfare of black Americans is an afterthought. Sue, the slaves themselves benefit from antislavery policies, but that's not why Northerners support them.