The primary difference between Socrates and the Sophists seems to lie in a disagreement on whether or not a truth (or knowledge) might be absolute.
Socrates (and Plato) pursued a line of rational thought intended to discover or determine real philosophical absolutes.
This belief in absolute truth(s) was epitomized in Plato's theory of the forms (which concerns the ideal/perfection of all things, including ideas). Through rational, logical pursuit a person might attain some insight as to the ideal, "true" form of any idea and thus be said to possess the truth.
This is, of course, a simplification of Platonic ideals and of the Socratic method, but it serves as a counterpoint to the Sophists.
The Sophists argued that truth and morality were relative. They "claimed that the value of actions varied according to circumstances, that knowledge was necessarily imperfect, and that truth was relative" (eNotes).
The political, moral and ethical ramifications of these distinctly opposed schools of thought should not be overlooked.
"The Sophists’ ethical relativism was sharply attacked by a new philosophical movement, led by Socrates, reaffirming absolute values" (eNotes)
Using Socrates as a vehicle in his writing, Plato developed the notion of the philosopher-king, describing an entire mode of government and ethics based on his idea of who might be best equipped to understand "right and wrong" and to rule correctly.
While Socrates is famously hailed as saying that wisdom is essentially an awareness of how little one knows, his position vis-a-vis absolute truth suggests that he viewed ultimate wisdom as an attainment of an ideal knowledge. The Sophists, for their part, argued against the existence (even potentially) of such an ideal form of knowledge.