This can all be explained as poor writing and forgetfulness on Bungie's side but,
How come your previous specific Guardian events of D1 are not referenced? How come Saladin doesn't recognize you? Why does your ghost sound different? Why are some subclasses slightly different? How come when you visit Hawthorn she only talks about defeating Ghaul and your clan and not the Black Garden, Crota, Oryx, etc, or how you're actually a legend? How come the Stranger doesn't frequently visit you and tell you new info about her war? And why aren't we Iron Lords hanging out at the temple?
It's because it's not the same Guardian as in D1. Sure you got to see your previous characters from D1, but soon as the story starts, and BEFORE the vaults are destroyed, you have completely different armour, weapons, ghost and a ship.
My theory is that following the events of D1, your Guardian has actually taken on the role of the Stranger in her apparent absence following the end of the vanilla story, a freelance Guardian, and that your D2 Guardian was simply in the right place at the right time. This also explains why locations from D1 aren't mentioned by your ghost, because your ghost never went to those locations.
Once again, this is probably all due to the fact that D2 was already being made while D1 DLC was still coming out, but I really enjoy trying to find logic in all this forgotten content. Perhaps our Guardian from D2 becomes the Stranger seen in D1 during the events of Osiris, with his timeline bending, fancy tricks, and Vex Multiverse? Meaning that D1 and D2 are happening concurrently in the same, but also different, non-linear timelines?
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Literally the first thing Shaxx says when he speaks to you is refer to you as Saladin's Young Wolf. Also, some dialogue is written as if you already existed, such as the Ghost speaking of Eris to Ikora in some Io missions related to the Taken.