Having looked at your map again I now think the blue overlay is the current river and the old bank boundary is the much wider thin line.
Not realising the overlay was the current state of play it is no wonder that when I measured it against the aerial photos they came out the same.
The river has had many buildings and businesses along the banks over the years and with wharves and docks being build and destroyed and rebuilt it is no wonder the artificial bank has moved.
The river is less likely to flood now too so the banks don't change like they could I guess, and the old map may show the maximum extent of the banks as they could be during the high tide or after a flood, buildings would be further back as they cannot be protected from the rising waters like they can these days.