You just have to suspend your disbelief and accept that it's a incarnation of the same guy, suited for the period of when the film is released. 1989's Licence to Kill referenced events from 1969's On Her Majesty's Secret Service, so...for what little sense it might make, Sean Connery, George Lazenby, Roger Moore, Timothy Dalton, and Pierce Brosnan were playing the same man.
I dislike it when people claim that "James Bond" is just a code-name handed down over the years or something. :laugh:
Casino Royale is excluded, obviously, which felt the freedom to chuck 40 years of Bond history to make their little Bourne knock-off work...:shakefist