if it's the same bass but "d string sounds different" then it cloud be many things
- different setup (string height, neck adjustment, pickup height etc. )
- different strings
- different technique
- different EQ
also: are you trying to produce a recording that matches this, or are you plugging into an amp in a room and hoping to match?
recorded always sounds different than live. Trying to match what you hear on a track with a live setup is quite a battle.
like I said you may have to be satisfied with a good approximation.
There are useful EQ lessons in that video I linked.