The determination of the classification of a firearm can, in principle, be done by anybody. Nobody owns that. Any person can look up the criteria that are in the Criminal Code and compare the characteristics of the firearm to those terms that are in the Criminal Code and arrive at a conclusion as to whether the firearm is non-restricted, restricted or prohibited.
However, for greater clarity and for the purposes of uniformity across the country, the RCMP keeps a database—the firearms reference table—which catalogues firearms and determines their classification according to the matrix in the Criminal Code. That is available to police, to officials and to the general public for their reference.
To answer the other part of your question, the actual assessment is made depending on exactly what the criteria are. If you are looking at one of the items—clauses 1 to 94, for example, or clauses 97 and onwards in the proposed schedule—those are based on the principal model of the firearm being named, and then any variant or modified version of it is also included. The exercise in classification would be based on whether or not the firearm in question was related to the original firearm in a way that would include it within the bounds of a variant or modified version.
In the case of 95 and 96, there are explicit physical criteria, and the question would be to accurately determine the diameter of the bore or the energy of the projectile, as the case may be. The firearm is then classified depending on whether it's over the thresholds or not.