Question Difference between database systems ?

Ones TR and the other isn't?

What makes you ask the question? It looks like you want help with homework. Are you asking for a school reason or business? Narrow the question some and I'm sure someone can help you.
 
Where, exactly, did you come across these terms?
Here the source:
In 1974, IBM began developing System R, a research project to develop a prototype RDBMS. The first system sold as an RDBMS was Multics Relational Data Store (June 1976). Oracle was released in 1979 by Relational Software, now Oracle Corporation Ingres and IBM BS12 followed. Other examples of an RDBMS include IBM Db2, SAP Sybase ASE, and Informix. In 1984, the first RDBMS for Macintosh began being developed, code-named Silver Surfer, and was released in 1987 as 4th Dimension and known today as 4D.

The first systems that were relatively faithful implementations of the relational model were from:

  • University of Michigan – Micro DBMS (1969)
  • Massachusetts Institute of Technology (1971)[9]
  • IBM UK Scientific Centre at Peterlee – IS1 (1970–72) and its successor, PRTV (1973–79)
The most common definition of an RDBMS is a product that presents a view of data as a collection of rows and columns, even if it is not based strictly upon relational theory. By this definition, RDBMS products typically implement some but not all of Codd's 12 rules.

A second school of thought argues that if a database does not implement all of Codd's rules (or the current understanding on the relational model, as expressed by Christopher J. Date, Hugh Darwen and others), it is not relational. This view, shared by many theorists and other strict adherents to Codd's principles, would disqualify most DBMSs as not relational. For clarification, they often refer to some RDBMSs as truly-relational database management systems (TRDBMS), naming others pseudo-relational database management systems (PRDBMS).

As of 2009, most commercial relational DBMSs employ SQL as their query language.

Alternative query languages have been proposed and implemented, notably the pre-1996 implementation of Ingres QUEL.
 
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Again, that reads like a text book. What is making you ask the question? Do you need homework help? Or is there a business question here?
That is not a homework assignment or business question, that is question of English reading comprehension. I don't speak English so it is difficult to me, to understand texts in English.
 
Without getting too far into the weeds of database design and theory:

" "truly-relational database management systems" (TRDBMS) " is really really strictly relational.
While "DBMS" is the generic abbreviation for a database management system. Which may or may not be relational.
 
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Without getting too far into the weeds of database design and theory:

" "truly-relational database management systems" (TRDBMS) " is really really strictly relational.
While "DBMS" is the generic abbreviation for a database management system. Which may or may not be relational.
Thanks, now its more clear.
Nice.