Dionysus vs Bacchus

Is Bacchus the same as Dionysus? In myth, yes — Ovid's Bacchus is born of Semele and Jove's thigh, turns the Tyrrhenian pirates into dolphins as in the Homeric Hymn, and has Pentheus torn apart as in Apollodorus. In Latin use, no — Virgil's Amata feigns "the madness Bacchus loves" to start a Latin war, and "Bacchus" in Latin can simply mean wine.