The first term διάβολος (from which our 'devil' comes) comes from the Greek verb "to slander" (διαβάλλω) and is definitely more common in the Septuagint as a translation for השטן. The second term σατανᾶς is obviously from the Hebrew (or more likely the Aramaic סטנא) and is a NT innovation apparently. Because it is Semitic sounding, the second might appeal more to authors such as Matthew, who likes to use Jewish terminology to give their gospel an "authentic" flavor. For example, in the story of Jesus' temptation, Matthew and Mark both use σατανᾶς, while Luke, the responsible Greek historian, changes it to διάβολος. But this is not a strong argument since σατανᾶς appears 36 times in diverse places in the NT (including Luke) without any kind of consistency (e.g., 2 Cor 12:7, Luke 10:18, 1 Tim 1:20 Rev 2:9). One very interesting use of διάβολος is found in John 6:70 where a human being (Judas) is referred to as the devil, but this is quite unique.
So the best I can say is that the two words are synonymous. They both mean the adversary, the enemy, the one who accuses the human race before God. This is very much in line with the image of השטן found in the Hebrew Bible (Job 1 and Zechariah 3).