The balance wire between the 2 sets of cells in parallel is just a wire so the equipment can read the voltages of each group of parallel cells independently. Exactly the same as using a voltmeter to measure the 1st 4 cells in parallel and then the 2nd set.
If you take a volt meter and measure then wire #1 and wire #2 you'll get the voltage of the 1st group of 4 cells - somewhere between 3.0v and 4.2v. Notice that #1 will be negative and #2 will be positive.
If you use the volt meter to measure #2 and #3 you again get somewhere between 3.0v and 4.2v that shows the 2nd group of 4 cells. Notice that #2 will be the negative and #3 will be positive.
#2 wire can be
both the positive for 1 measurement and the negative for the 2nd measurement at the same time - e.g. if you have 2 voltmeters, you can measure both groups of 4 cells in parallel at the same time to demonstrate this.
If you measure from #1 to #3 you get's the 6.0v to 8.4v - as this is the same as the main load/charge wiring.
Get a voltmeter and try it out! It's perfectly safe.
View attachment 33597
The BMS and the Charger balance port use wires #1, #2, and #3 the same as the volt meter experiment above - to see the voltage on each group of 4 cells in parallel - independent of each other so they can maintain balance between the parallel groups of cells. Balance means that if group 1 is 3.71v then group 2 should also be very close to 3.7v at the same time for a healthy / safe battery.