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There is more of a distinction.
After Socrates, there was a tendency to more specialization. Some Greek philosophers focused---sometimes almost exclusively---on natural philosophy (which can also be called ancient Greek science) and/or ancient Greek mathematics and some, like Socrates, focused---sometimes almost exclusively---on ethics and theology.
It is also true that Presocratics are distinguished by the fact that writings of even the most important ones are lost, except for fragments. This makes them more mysterious and oracular.
Also arguably the Presocratics were more creative, less inhibited by the theories of the mighty dead.
Very importantly, because they came earliest to natural philosophy, Presocratics are fascinating in the history of science as showing how science began: Principium Sapentiae.
See Principium Sapentiae: The Origins of Greek Philosophical Thought (1952) by F.M. Cornford (1874--1943) and W.K.C. Guthrie (1906--1981). It is one of those seminal books that remain readable even though much now has be corrected by later work. Historian of science David Furley (1922--2010) stated it was one of the books that stimulated his research even though it contained much he would disagree with later on (see Fu-164). See Principium Sapientiae: The Origins of Greek Philosophical Thought by F. M. Cornford, W. K. C. Guthrie: Review by: D. A. Rees.
He counts as a Presocratic because of his early interest in natural philosophy (and because he wrote nothing at all) and he is ex officio a "Socratic philosopher".