Robert
I am assuming you have some (or all) of the original button head style grease fittings. There were two sizes: regular and large. The carrier uses regular which I see also are referred to as 5/8".
When you say your Canadian Tire grease gun works on some of the fittings, then that means someone has changed some (or all?) of your fittings over to the nipple style. In that case the Cdn tire end will work on any of them, although angles of access may require you to get some flexible coupling.
In the photo below is one with a dozen various grease nipples and one button head fitting. In the other photo is a button head fitting.
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