Here's an excerpt of what I found on the SEP on Presocratic Philosophy:
Calling this group “Presocratic philosophers” raises certain difficulties. The term was made current by Hermann Diels in the nineteenth century, and was meant to mark a contrast between Socrates who was interested in moral problems, and his predecessors, who were supposed to be primarily concerned with cosmological and physical speculation. “Presocratic,” if taken strictly as a chronological term, is not quite accurate, for the last of them were contemporaneous with Socrates and even Plato. Moreover, several of the early Greek thinkers explored questions about ethics and the best way to live a human life. The term may also suggest that these thinkers are somehow inferior to Socrates and Plato, of interest only as their predecessors, and its suggestion of archaism may imply that philosophy only becomes interesting when we arrive at the classical period of Plato and Aristotle. Some scholars now deliberately avoid the term, but if we take it to refer to the early Greek thinkers who were not influenced by the views of Socrates, whether his predecessors or contemporaries, there is probably no harm in using it.
The Presocratics were 6th and 5th century BCE Greek thinkers (starting with the Milesian school), while the hellenistic period went well over into the Common Era (the first 400 years, roughly, were the era of hellenistic Christianity) and contains Greek as well as Latin philosophers. To be precise, "hellenistic philosophy is the period of Western philosophy that was developed in the Hellenistic civilization following Aristotle and ending with the beginning of Neoplatonism" (Wikipedia), so the pre-socratic thinkers aren't part of the group.