Divisional Performance Measurement

Is it true that there are different types of divisions such as:

1) Cost divisions (ie cost centres):
It is where the manager has control over costs only (ie cost reduction / cost variances / other cost control techniques)

2) Revenue divisions (ie revenue centres)
It is where the manager has control over revenues (ie increase or decrease in selling price / production capacity)

3) Profit divisions (ie profit centres):
It is where the manager has control over revenues + costs (ie choosing suppliers)

4) Investment divisions (ie investment centres):
It is where the manager has control over revenues + costs + new capital investment (ie investment in new machines)

In Divisional Performance Measurement, we are concerned with measuring the performance of an investment division (or particularly the manager of the investment division).

To evaluate the performance of the divisional managers both the financial and non-financial measures are calculated for assessing the performance of the manager.

Is that all correct?