What is this expression changing process?
Broadly, this is known as standardization or normalization.

Examples of this include (for expressions) Conjunctive Normal Form and Disjunctive Normal Form.

There is no Microsoft documentation I am aware of that lists all the steps of the multiple processes involved. Essentially, SQL Server converts things into a standard format to make things easier for it to work with internally. This occurs at various times, including during parsing, and the normalization stage of query compilation and optimization.

As far as CAST versus CONVERT is concerned, it may simply be that CONVERT was first (and/or because it offers a superset of functionality). You should find that built-in (intrinsic) functions are generally preferred.