As is typical with the oral tradition of tale-telling, the details got muddled. Theodoric was born shortly after Attila the Hun died and a century after the Gothic King Ermanaric; he later invaded Italy and became its "king" by defeating Odoacer (the previous invader), with his capital in Ravenna. Dietrich, on the other hand, was the king of Italy already, ruling from Verona, but was forced into exile by his evil uncle, Ermenrich, and winds up at the court of Etzel (Attila) and the Huns. The switch from Ravenna to Verona suggests that the legends arose from the Lombards, whose capital was Verona (Ravenna was still part of the Byzantine culture).
Dietrich also differed from Theodoric in that he sometimes was depicted as breathing fire. This suggests a hint of the demonic. There may be an origin of this in some of the ideas about Theodoric. A 12th-century German chronicler, Otto of Freising, wrote that Theodoric rode to Hell (while alive) on an "infernal" horse. (See the illustration, thought to represent that ride of Theodoric, who is here labeled regem stultum, "stupid king," on the church portal of San Zeno Maggiore in Verona.) Some traditions called Theodoric a son of the devil. Because Theodoric was a practicing Arian, the prevailing Roman Christianity had reasons to "demonize" him.
An early (c.820) German heroic lay, Hildebrandslied, includes the story of the main character's flight alongside Dietrich to escape Odoacer, one of the few people that handed Theodoric defeats (until Theodoric negotiated a treaty and then slew Odoacer during the celebratory feast). Later legends become less and less historical, with Theodoric/Dietrich slaying a dragon, or fighting dwarves and giants.
The Church of San Zeno Maggiore, whence comes the above illustration, has a few more interesting historical tidbits I'd like to share. At first I thought it might be linked to Zeno, the Byzantine Emperor who put Theodoric in charge of the military and set him against Odoacer, but it turns out that it's a lot more interesting than that. See you tomorrow.