MPPT display voltage vs actual battery level
All batteries have an internal resistance which drops more and more voltage as the load draws more and more current. 

In your case, let's say the battery reading is 13 volts unloaded and 12.4 volts with 8 amperes into your load.

Under those conditions, the battery's internal resistance would be:

$$ R_{INT} = \frac{V_{BAT} - V_{LOAD}}{I_{LOAD}} = \frac{13V - 12.4V} {8A} = 0.075\text { ohms} $$ 

As for discharging a battery, the terminal voltage depends on your battery's chemistry, capacity, and how much current you take from it. Rule of thumb for sealed lead-acid is to never let the voltage fall below 10.5 volts. 

Assuming yours is sealed lead-acid, here's a pretty good link.

There's also a lot of information here