"An index is a copy of select columns of data from a table that can be searched very efficiently that also includes a low-level disk block address or direct link to the complete row of data it was copied from." [1]
When you reference a field in an index, you're effectively duplicating this column on disk.
We can discuss semantics, but at the end of the day, indexes are glorified copies of your columns in a specific order.
- It's done at the hard disk level, so no database or data schema is involved.
- It's not done for performance reasons, but for security reasons (not to lose any data).
"In computing, denormalization is the process of trying to improve the read performance of a database, at the expense of losing some write performance, by adding redundant copies of data or by grouping data."
It's a technique that involves copying data for some very particular reason, an abstraction to hide the nasty duplication because the desirable thing is to have only one source of truth.
So while there's some remote similarity (the copying of data), the goals are completely different.
They are denormalized data, sort of.