I'll take a stab at this question, and hopefully provide you with a basic answer.
Currently, there is only one Engineer Support Regiment in the Canadian Army, which is 4 Engineer Support Regiment, based at Gagetown.
The basic difference between 4 ESR and the Combat Engineer Regiments, is that, 4 ESR's primary operational role is to provide general support to the Canadian Army both at home and abroad. 4 ESR also provides field engineer and field engineer equipment support to CFB Gagetown and Land Force Atlantic Area.
4 ESR, also has four Area Construction Troops spread across Canada, one in each Land Force Area (1 Area Construction Troop - LFWA (Edmonton), 2 Area Construction Troop - LFCA (Petawawa), 4 Area Construction Troop - LFAA (Oromocto), and 5 Area Construction Troop - LFQA (Valcartier).
The role of the Combat Engineer Regiments within the Canadian Army, currently, whether Regular (1 (1 CMBG), 2 (2 CMBG), and 5 (5 CMBG) CER) or Reserve (31 (31 CBG), 32 (32 CBG), 33 (33 CBG), 34 (34 CBG), 35 (35 CBG), 39 (39 CBG), and 41 (41 CBG) CER), is the field engineer support of the brigade group to which they are a component part of.
Presently, three of the Reserve brigade groups, are supported by an Engineer Squadron, and not a Combat Engineer Regiment, which are 36 CBG - 45 Engineer Squadron, 37 CBG - 56 Engineer Squadron, and 38 CBG - 31 Engineer Squadron.