What is this Formal Patent Search of Classification? I haven't been
able to find any information on it online. Does it differ from a
preliminary patent search (as explained on the CIPO website) in any
meaningful way?
A patent classification is a system to categorize (code) documents, such as published patent applications, according to the technical features of their content. Patent classifications make it feasible to search quickly for documents about earlier disclosures similar to or related to the invention for which a patent is applied for, and to track technological trends in patent applications.
Searches based on patent classifications can identify documents of different languages by using the codes (classes) of the system, rather than words.
The International Patent Classification (IPC) is agreed internationally. There are other additional patent classifications such as The United States Patent Classification (USPC) is fixed by the United States Patent and Trademark Office (USPTO). The Derwent classification system is fixed by an enterprise. The German Patent Classification (DPK) was fixed by the German Patent Office. European Patent Office (EPO) and USPTO launched a joint project to create the Cooperative Patent Classification (CPC).
In simple term Patent applications are classified in classification schemes on the basis of their technical content. They are assigned classification symbols.
The code as broadly classified as below which have classes, subclasses, sections
A HUMAN NECESSITIES
B PERFORMING OPERATIONS; TRANSPORTING
C CHEMISTRY; METALLURGY
D TEXTILES; PAPER
E FIXED CONSTRUCTIONS
F MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
G PHYSICS
H ELECTRICITY
For example A43B1/0054 is code for Footwear provided with magnets, magnetic parts or magnetic substances. This makes it easier to manage and to search for patent applications in a given technical field. If your technology falls under mechanical the code would start with F followed by class and subclass.