>>15131862
They don't really go too far into that, probably to keep the magic of "is he really alive, with feelings?" Question going, but it seems to be divided into basic, and advanced Titans.
The basic titans are those fielded in Titanfall 1, the Atlas, the Ogre, and the Stryder. They show a high capacity for modular upgrades, but aren't shown to be particularly unique in any way, intelligence included. They can be modified with different AI cores, so this could be rectified with an expensive enough core, but none of them are shown to be long term, unique intelligences, being more like a Droid from Star Wars; wiped often enough they don't develop a real personality with quirks.
Titanfall 2 titans are apparently unique to their chassis, which is much harder to replace than a datacore. We are also introduced to the concept of a removable core, though it isn't confirmed if this is unique to the Vanguard class. We are, however shown a fair amount of variability in how the titans behave, with more combat maneuvers when set autonomously, and a greater sense of battlefield awareness shown in their radio communications.
My overall theory is that every titan in the multiplayer is indeed uniquely yours, and the justification for their AI surviving destruction, even when you don't retrieve the datacore like you did with BT, is that they are storing themselves wirelessly in your pilot gear, like BT does at the end of the campaign. The Advanced style chassis are said by BT to be "highly advanced" gear, so it could be that BTs AI core is actually an archaic solution to a problem that the IMC had solved ages ago, and his survival at the end was reached though his self ingenuity.