The only wires a battery has are the out put wires to the controller, one Red & one Black. These are in your pic with the Blue bullet connectors.
The three you show are controller to peripheral connector's, left Black Julet 8 pin is 1T4 trunk cable connector for lcd, throttle and brakes. The Yellow Julet is PAS and the Female large Julet is hub motor cable (extension) connector, all three are only found on controller's.
For battery replacement any generic type can be used and all will have just the Red & Black out put wiring, all you have to do is check polarity is correct with a metre and then connect controller.