The two Vegetii

[Renatus]

Also, the fact that we have both names does rather point to different men (though perhaps related) rather than both being the same.

All manuscripts of the Mulomedicina are attributed to Publius, while all but one of the manuscripts of the Epitoma are attributed to Flavius.  It has been suggested that Flavius is an honorific title denoting Vegetius' status in the late-Roman hierarchy and that the full rendition of his name would be Flavius Publius Vegetius Renatus. I tend to think that they are different people and  have suggested (with my tongue only partially in my cheek) that they were brothers and that any similarity in  their styles, which some scholars have observed, is due to their having the same tutor.

He sort of glosses over it but states that improvements to Roman cavalry had been provided by the Goths, Alans, and Huns (one of the reasons I think he wrote for Valentinian III in the late 430's).

You don't have to go as late as Valentinian III to find these tribes.  Ammianus Marcellinus mentions them as being involved in the battle of Adrianople.