William Hartnell and Jo Martin are multiverse versions of the same doctor. First one after the Irish police one in division. 

Both stayed in division after that. Hartnell sent to investigate what division believe to be a rogue time Lord which turns out to be the doctors daughter from tenth era story. 

Is ordered to lead her into trap to eliminate her but for first time his moral code develops and becomes the doctor. 

In an attempt to cover up her identity he forces a regeneration on her and she becomes Susan who he es off as his granddaughter. This is successfully for a while but is in danger of being exposed by the master so this is why the doctor runs away with Susan and ends up in totters yard as a fugitive. 

Martins doctor continues in division and is told to investigate a rogue time lord but gets misdirected by ravagers. Ends up tracking 11th doctor in other universe. Tracks and researches and realises who he is and where he is in regeneration cycle. 

Speech from Clara about loving doctor makes sense in this now as time Lords clearly never loved the doctor. Martins doctor betrays tecteun to get the secret of extra regeneration cycle which he hasn't got in this universe. Tecteun now has clear grudge against Martins doctor and this is why she runs from division into the other universe. 

The master has moved 13 into the alternate universe and is misleading her by showing her a vision of gallifrey in the other universe. The lost memories that are stored in the fob watch are memories of hartnell as young division agent and the truth about Susan