Great question.
Current ACI design (2002 onwards) is based on strain limit and based on that you end up with tension controlled or compression controlled sections. Tension controlled being the sections where strain is steel is equal or greater than the limit provided by code (0.005 I believe).
Previously (1963 to 2002), the reinforcement design was based on reinforcement ratios. This is where the terminology "under-reinforced", "over reinforced" and "balanced reinforcement" comes from.
The simplest word to put this is that any steel that has strain greater than 0.005 (or whatever the code says) at time of concrete failure is termed as tension controlled. Both under-reinforced and balanced reinforcement sections will meet this criteria.