Wow! Grown from seed! That is super fun Adam!!! I lost my Pachypodium saundersii this year.. So just focusing on my Adeniums..will try to re-visit Pachypodiums next time. Failure in my overwintering indoors..

This really seem to be the defining characteristic:

"Most species of cacti have lost true leaves, retaining only spines, which are highly modified leaves. As well as defending against herbivores, spines help prevent water loss by reducing air flow close to the cactus and providing some shade. Cactus spines are produced from specialized structures called areoles, a kind of highly reduced branch. Areoles are an identifying feature of cacti."
- http://en.wikipedia.org/wiki/C...

Yes, that is one of the defining traits of a cacti. It just gets confusing when the cacti comes in different shapes or if one do not understand what an areole is. I just go with, if it has spines all over particularly on its stem, assume for awhile it is cacti, till confirmed otherwise. Other traits will later reveal itself..color of sap, if it blooms etc.

Now that euphorbias aren't cacti its anyone's guess