Balanced take off has nothing to do with characteristics of an airfield but everything with the actual performance of the aircraft in terms of a chosen V1.
Once these data are set they are compared to the TODA and ASDA to make the take off legal but these are two different issues.
The calculation of V1 so TOD=ASD is the only process that balances the take off, verifying that the TOD and ASD are lower than TODA and ASDA in not a performance calculation at all, as such there is only one correct definition and it's important that this is clearly understood.