In a true "sandbox", the player has tools to modify the world themselves and create how they play. So along with open world PvP, they'd have to add the option for user generated content. Think "GTA Online". This is my first MMO so I wouldn't know what a sandbox MMO would be like. But there are plenty of sandbox console games.
Not sure how you create content in GTA (but then, I stopped following the series after maybe 3 hours of GTA4, because it was too boring for me, unlike San Andreas), but I basically your explanation is correct.
Explanation of Sandbox for you Ghoul_drool
Good example is the now very popular Minecraft
(I am sure you heard of if, if now, where were you hiding for the past 2 years?), where you can literally build anything you want from whatever materials you have. You also have the possibility to play with other people in multiplayer and kill them or destroy their stuff.
Or perhaps even better example would be SPORE
, conceived by Will Wright (the guy behind Sims, SimCity, etc), where you created anything from lifeforms to spaceships, and then you used those for playing. However, there was no multiplayer per se (you could use and meet other people's creations, but you could not play with others directly)