Well, it's an interesting distinction, but I wonder, does it make a difference?
Consider for a moment, if you were a Virginian who thinks there is a movement afoot in the North to impair your political ability to resist tariffs (e.g., the Morill Tariff), work your plantation, and be secure in your bed at night, is there a useful distinction to be made between limousine-liberal spewers like Garrison and Wendell Phillips, both of whom publicly cursed the Constitution and made their contempt for it known? Phillips pulled this stunt in 1842, Garrison in 1851, both of them failing to decline, on principle, the protections of the republic afterward, however, or to seek the protection of some European power.
The point of distinguishing between an abolitionist and an Abolitionist, if you insist on a distinction, would be to show someone on the other side some reason to apprehend the approach of the one, but not the other. But as we have seen from the progress of Republicanism from 1856 to 1868, the fulminations of the most ardent abolitionists were shorn of the trappings of power, whereas the policies of Abraham Lincoln were decidedly not.
From some abolitionists, the Southern planters received incendiary pamphlets and rhetoric. From Lincoln, authentic fire and sword. If I had to choose, I'd name the fire-eaters as the "small-A" abolitionists, and capitalize the title for Lincoln and Grant and their two-million-man army.
However, once the war began, they viewed slavery as the underlying cause and moved more toward the radicals in favoring the rapid ending of slavery. U.S. Grant may have said it best.
"In all this I can see but the doom of slavery. The North do not want, nor will they want, to interfere with the institution. But they will refuse for all time to give it protection unless the South shall return soon to their allegiance." -
April 19, 1861, in a letter to his father-in-law, Frederick Dent.