Business process management is a common term. But it is rarely questioned what sense bears each word in this combination. Does it imply to manage business with processes? Or to manage business processes? Or to enable processes managing business? Perhaps, nothing from above.
In fact, it might be silly to manage business processes, as far as they do not strictly correspond to real process execution. Therefore, the key for interpretation here is proper governance. Control of execution is the required condition to make sense in process management.
On another hand, rigid control may also turn process management into a nonsense. It is well known that real process execution never coincides exactly with an ideal schema. To account for this natural variability, flexible case management must be also in place.
Perhaps, the most relevant word here might be not management but alignment. Processes in a company must be well documented and aligned along designed schemes and guidelines. Deviations from the schema must not be considered negatively, as far as it does not harm established performance metrics for a process.
The goal of efficient process management is to achieve a natural balance, alignment and harmony between business and its processes.