Here's quote from an online etymological dictionary. Might explain it better than I can, no?
"Slav
1387, Sclave, from M.L. Sclavus (c.800), from Byzantine Gk. Sklabos (c.580), from O.Slav. Sloveninu "a Slav," probably related to slovo "word, speech," which suggests the name originally meant member of a speech community (cf. O.C.S. Nemici "Germans," related to nemu "dumb"). Identical with the -slav in personal names (e.g. Rus. Miroslav, lit. "peaceful fame;" Mstislav, lit. "vengeful fame;" Jaroslav, lit. "famed for fury;" Czech Bohuslav, lit. "God's glory;" and cf. Wenceslas). Spelled Slave c.1788-1866, infl. by Fr. and Ger. Slave. Adj. Slavic is attested from 1813; earlier Slavonic (c.1645), from Slavonia, a region of Croatia.
slave (n.)
c.1290, "person who is the property of another," from O.Fr. esclave, from M.L. Sclavus "slave" (cf. It. schiavo, Fr. esclave, Sp. esclavo), originally "Slav" (see Slav), so called because of the many Slavs sold into slavery by conquering peoples.
"This sense development arose in the consequence of the wars waged by Otto the Great and his successors against the Slavs, a great number of whom they took captive and sold into slavery." [Klein] "