If the ECU is ‘Engine Control Unit’, why should I fix it if the problem is not with the engine, but with the transmission?

In the case of the automatic 2001-2003 Toyota RAV4 models, the ECM controls both, the engine and the transmission. In other automatic car models and brands, there are two separated units, one for each part. The engine unit would be the ECM or ECU and the transmission unit would be the TCM or TCU.