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Given a rechargeable 2000mA NiMH AA battery at 1.25v it measures 8.0A. Did the multimeter try to pull 10A from the battery but measured that the battery could only provide 8.0A?
Other answers have stated that you shouldn't do it, but not what you actually did:
What you did was you short-circuited the battery and measured the current through the short circuit. Your battery was able to put 8 amps through a short circuit.
There's no need to think of it as "multimeter tried to pull".
Some types of batteries can explode when short-circuited, hence the danger.
What you did, depending on battery chemistry, was very bad: the consequences could have been an explosion or fire.
Testing a battery of any type would be in this fashion:
apply a known rated load for a given time (rated to some fraction of the battery capacity and AH rating), vehicle lead acid batteries (trucks etc) can provide 1000A or more so make sure the loads are chosen suitably.
measure the voltage, current and time.
Calculate the result as needed. Repeat at various intervals of time and / or voltage - be aware of voltage and current limits for the type of battery tested.
This procedure must be tailored to the battery chemistry under test, what is valid for one battery may not be safe for another. Fuses etc should be used liberally as well as ppe (personal protective equipment).
If you want to measure the internal impedance of the battery (here limited to 200 A) and/or the maximum current that the battery could "give", one could use a circuit like this (be aware of "safety" ... and power on the resistor and active devices),
this circuit can sink 1000 A if the battery is in very good conditions).
Adjust pulse (100 us or less) width and period, with a very low "Duty Cycle" ( D < 0.001).
NB: I show the behavior with a "ramp", which should be preferably a "pulse".
An MCU should be used to measure the variables needed for calculating impedance.
Did the multimeter try to pull 10A from the battery but measured that the battery could only provide 8.0A?Yes, the DMM tried to draw as much current as possible (because the battery is basically shorted), but it was limited to 8A by the shunt resistor of the DMM and the output resistance of your battery. I don't know what kind of battery (chemical, capacity, etc) you have but you must be lucky, because this could have been ended with fire or explosion. What did you try to measure, actually? \$\endgroup\$