As you all know the Titanic's wreck site is located at 41.43N and 49.56W, but how the ice gets there? There's a permanent but ever changing cold water tongue of the Labrador Current there. This cold water tongue is actually a cold-core eddy or a meander or whatever you call it. If the ice
does travel so far southward and westward it
always occupies the center of this eddy ( the water is much warmer outside of the cold core of an eddy, the ice will not survive there and besides cold-core eddies trap the ice inside them.). Sometimes there could be an eddy inside an eddy , but for now I will not discuss this case.
So as you see from this 1914 chart the ice gets there traveling around on the left-hand side of the eddy, where the currents run to SW. Both Titanic and Californian were at the right-hand side of the eddy. They both were affected by north-eastern currents, with some variation (more north or more east). IMO this explains the discrepancy of the Titanic's SOS position.They did not account for currents that probably were stronger than usually. The both-eastern currents also nicely explain why
Carpathia saw the green flare on her starboard side. The wreckage found south of the wreck site could have been brought there by wind that started at 4 a.m. or by smaller features that are located inside this tongue (and there are a lot of them).
The Californian was probably not affected by southern drift (unless she traveled around another eddy, which IMO is unlikely) until she reached the ice field. I believe that at 19:30 (when Californian took their position by Polaris) they could have noticed that the currents took them to the north of where they wanted to be and they adjusted they course a little bit too much. Another possibility they moved south because they believed there were less icebergs there. After the collision there was probably very little drift for the Titanic because there is no current so close to eddies' centers. The Californian was probably affect by the currents explained here
Approaching and retreating Californian explained
The four Aprils 14 images below show the currents for a few years. As you see the shapes and the sizes of cold water tongues in them are different, but every year there were north-eastern currents on the way of all three ships: Californian, Titanic and
Carpathia.