Perhaps this will come as a surprise to some, but I actually do find the use of the term table in common table expression as very appropriate. In fact, I find the use of the term table expression as appropriate. To me, the best way to describe what a CTE is in T-SQL, it’s a named table expression. The same applies to what T-SQL calls derived tables (the specific language construct as opposed to the general idea), views and inline TVFs. They are all named table expressions.
If you can bear with me a bit, I’ll provide the reasoning for my view of things in this article. It occurred to me that both the naming confusion, and the confusion around whether there’s a persistency aspect to table expressions, can be cleared with a better understanding of the fundamentals of our field of relational database management systems. Those fundamentals being, relational theory, how SQL (the standard language) relates to it, and how the T-SQL dialect used in the SQL Server and Azure SQL Database implementations relates to both.
There’s a lot of depth in this post, so I recommend a careful reading.