• Only the RDM satisfies the definition;
• The E/RM can be used at the conceptual level to model reality, the latter can be used to model data at the logical level (i.e., formalize conceptual models as logical models for database representation).

• Understanding Conceptual vs. Data Modeling Part 1: The E/RM and the RDM.
• Understanding Conceptual vs. Data Modeling Part 2: The E/RM Models Reality, the RDM Models Data.

• Understanding Conceptual vs. Data Modeling Part 3: Don't Conflate Reality and Data.
• Understanding Conceptual vs. Data Modeling Part 4: Property-Entity Modeling.

“The E/RM is not a data model as formally defined by Codd: no explicit structural component except sets classified in various ways, no explicit manipulative component except implied set operations, and very limited integrity (keys).”

--David McGoveran

“[It] is not even clear that the E/R "model" is truly a data model at all, at least in the sense in which we have been using that term in this book so far (i.e., as a formal system involving structural, integrity, and manipulative aspects). Certainly the term "E/R modeling" is usually taken to mean the process of deciding the structure (only) of the database, although [it does deal with] certain integrity aspects also, mostly having to do with keys ... However, a charitable reading of [Chen's original E/RM paper] would suggest that the E/R model is indeed a data model, but one that is essentially just a thin layer on top of the relational model (it is certainly not a candidate for replacing the relational model, as some have suggested).”[2]

“What is the difference between an index and a key? How are they related?”

“There seams to be some confusion between what a Primary Key is, and what an Index is and how they are used. The Primary Key is a logical object. By that I mean that is simply defines a set of properties on one column or a set of columns to require that the columns which make up the primary key are unique and that none of them are null. Because they are unique and not null, these values (or value if your primary key is a single column) can then be used to identify a single row in the table every time. In most if not all database platforms the Primary Key will have an index created on it. An index on the other hand doesn’t define uniqueness. An index is used to more quickly find rows in the table based on the values which are part of the index. When you create an index within the database, you are creating a physical object which is being saved to disk.”

“A primary key by default creates a clustered index. A unique constraint/key by default creates a non-clustered index.”

“An index is a (logically) ordered list of rows. For example, an index on LastName means all values are already sorted in LastName order. Usually index rows contain far fewer columns in them than the table itself (except the clustered index, which is the table). A key is a column or columns that defines the order of an index. For example, on an index ordered by (LastName,FirstName), then LastName and FirstName are the keys. Btw, a primary key is a physical object, not a logical one. The db engine needs physical rows in order to insure unique values in the index.”

--Difference between an index and a key?, SQLTeam.com

"As a relational feature, keys can only be properly understood within the formal foundation of the RDM, which is simple set theory (SST) expressible in first order predicate logic (FOPL) adapted and applied to database management. Yet that is precisely what is ignored and dismissed in the industry -- including by the authors of SQL[3]."

“One of the things that confuse SQL users all the time is how DISTINCT and ORDER BY are related in a SQL query ... most people quickly understand:
   

SELECT DISTINCT length
FROM film

[that] returns results in an arbitrary order, because the database can (and might apply hashing rather than ordering to remove duplicates) ... Most people also understand:
   

SELECT length
FROM film
ORDER BY length

[that] will give us duplicates, but in order ... And, of course, we can combine the two:
   

SELECT DISTINCT length
FROM film
ORDER BY length

[But if] somewhat intuitively, we may want to order the lengths differently, e.g. by title:
   

SELECT DISTINCT length
FROM film
ORDER BY title

[m]ost databases [sic] fail this query with an exception like Oracle’s:

ORA-01791: not a SELECTed expression

At first sight ... this

SELECT length
FROM film
ORDER BY title

works after all ... So, how are these different? We have to rewind and check out the logical order of SQL operations (as opposed to the syntactic order). And always remember, this is the logical order, not the actual order executed by the optimiser.”

--How SQL DISTINCT and ORDER BY are Related, Jooq.org