The other nomenclature note to make is the distinction between a CER and FER. While we're going full speed ahead at bastardizing the naming to suit what sounds cool, there is a clear definition for each (admittedly, this comes from Corps 86, so take it FWIW).
The FER is an organization that provides close support to infantry formations. Similarly, the AER (armd engr regt) provides close support to armoured formations. The ESR is the divisional level general support engineering organization.
The CER is the (engineer) combined arms organization that involves a mixing of field (infantry supporting), armoured (tank supporting), and general support engineers into one organization. So, a true CER doesn't really exist outside of 1 CER at the moment, and likely won't ever in the reserve world.
It's the same process of devolution that has us adopting the term CMBG, which originally denoted the Corps Mechanized Brigade Group (essentially, the corps reserve). In our normal Canadian doctrinal bastardization, we change the Corps to Canadian and keep marching.