A regular force infantry company belongs to a battalion, which usually has three rifle companies, a combat service support company and a headquarters/combat support company. That battalion is both the administrative home of all the soldiers serving in it but also a tactical entity that can manoeuvre on the battlefield.
Each of the nine regular force infantry battalions come from one of the three Regiments: RCR, R22eR or PPCLI. Each of those regiments has three battalions who wear the same capbadge and share the same traditions (but there are little quirks here and there both from recent history and from the murky past of Unification when the earth was still cooling). They also serve as a way to manage the careers of the members of the infantry. Those regiments are not, however, tactical entities that would manoeuvre on the battlefield under "regimental control." The battalions belong in real-time to one of the three Canadian Mechanized Brigade Groups which have a mixture of infantry, armour, artillery , engineers, service support, signals/HQ and MPs. The Commanding Officers of the infantry battalions report to their Brigade Commander. I admit up front that I am glossing over some complexities but I hope you get the picture.
In the reserves, however, each Regiment is generally one "battalion", although in practice most muster a single company with a HQ element. There are some Regiments in the Reserves, I think, that have more than one "battalion" in another location. Those 2nd battalions have COs but, yet again, tend to be company strength. I believe that the Reserve structure is a bit of a hold-over from WW2.
Be warned - there are pages upon pages of threads on this site about reserve structure/restructure and why a reserve regiment/battalion has a single company. :worms: Tread not there, lest the wyrm take you!!!!!!!!