This has come up before, I'm sure, but there are in fact two different usages of the term "balanced field".
The more general usage seems to be that which refers to the takeoff performance characteristics of the aircraft, in which case the term "balanced field length" is used when referring to a single takeoff field length, which is (either by design or by assumption) equal to both ASDR and TODR. It will be "by design" if the OEM or the operator is scheduling V1 such that the two distances "balance". It is "by assumption" where they are in fact different (and perhaps cannot in fact be equal) but regardless the assumption is made that "declared distance"=BFL=TODR=ASDR. In this latter case one is leaving some performance "on the table" for the simplicity of a single distance.
The more specialised usage seems to be mainly a British thing, and refers to the characteristics of the runway. In this case, the runway is said to be a "balanced field" if the ASDA=TODA.
The two terms actually have their uses, and in fact can be profitably used together provided one is careful and precise.
for example....
Aircraft X has a range of possible V1s, giving a range of ASDRs and TODRs which overlap. I can make my life simple and publish a single V1 for a given condition, such that TODR=ASDR for that condition. I have published the "balanced field length" for the aircraft.
I wish to know if I have optimal performance for airport Y. How can I find out? Well, ASDR=TODR is only optimum where TODA=ASDA. In other words, balanced field length data for the aircraft is only the best solution where the AIRPORT is a balanced field. If the field is not balanced I have to unbalance the aircraft if I am to optimise my takeoff performance.