DBMS vs computer software

DBMS and computer software both are nouns.

Word	Noun	Adjective	Verb	Adverb
DBMS	Yes	No	No	No
computer software	Yes	No	No	No

As nouns, computer software is a hypernym of DBMS; that is, computer software is a word with a broader meaning than DBMS:

DBMS: a software system that facilitates the creation and maintenance and use of an electronic database
computer software: (computer science) written programs or procedures or rules and associated documentation pertaining to the operation of a computer system and that are stored in read/write memory

Other hypernyms of DBMS include package, software, software package, software program, software system.

DBMS (noun)	computer software (noun)
a software system that facilitates the creation and maintenance and use of an electronic database	(computer science) written programs or procedures or rules and associated documentation pertaining to the operation of a computer system and that are stored in read/write memory