Yes, that's how I understand things. There are two separate plants.
Aloe vera was called Aloe barbadensis for a long time but it was discovered fairly recently that the "vera" name takes precedence because it was published first (taxonomists love these kinds of details). By a matter of weeks or months actually, as I remember things. No time at all in the big picture. So
Aloe vera = Aloe barbadensis (old name) (same plant)
As for the plant called chinensis, this is a different plant which also has medicinal properties (which are distinct). This is the relationship established by the 2011 "Definitive Guide" to the Aloes. (Which, in all fairness, does itself a disservice by showing a flower with the wrong color on the Aloe vera species page.)
Aloe officinalis = Aloe vera chinensis (old name) (same plant)
The bottom line is that there are two separate plants (currently separate species) which have in the past both been called Aloe vera, and both been called barbadensis. The differences have to do with the size (Aloe vera usually larger), the presence of spots on adults (Aloe vera adults are mostly unspotted), the flower color (Aloe vera is always yellow), the flower shape (Aloe vera is always ventricose, with a little belly on each flower), and the type of medicine (Aloe vera topical, Aloe officinalis consumed). And if your plant sets viable seed, it is not Aloe vera.
More than you wanted to know.