DBMS = Data Base Management System
There are all sorts of definitions abounding. ISO has published some guidelines regarding what is and what isn't a DBMS. But the truth is, not all vendors of products claiming to be a DBMS adhered to those standards. ANSI has defined some standards regarding SQL, which is the de facto language for modern DBMS usage. So you could do web searches for "database" and either ISO or ANSI (in a way that forces both to be part of the topic). You should be able to come up with a bunch. The link posted earlier is just one such example of web-available you can find if you just look.
A DBMS in PRACTICAL terms is any program or set of programs that manage a repository of data based on tabular storage concepts, and that support retrieval of that data in ways other than it was stored. Yes, that IS a very loose definition. It is NOT the industry standard definition. But it IS the definition promulgated by some vendors, especially of inferior products with delusions of grandeur. By this standard, Excel qualifies as a DBMS, although most folks here (including ME) would NOT qualify it as such. So my point here is, don't read the title on the box and think it is a DBMS. Look at its features, its properties. See what it does before you decide it is or isn't a DBMS in your eyes.
Access IS an example of a DBMS that happens to be mostly self-contained (except that it allows external references). It is NOT, however, a large-scale DBMS. It is targeted for a smaller environment.
ORACLE, SYBASE, Ingres, DB2, FOCUS, Paradox, RDB, MS SQL Server, ShareBase (if you can still find one...) - all of these qualify in some form or another as a database management system.
ORACLE directly supports tables, queries, and certain types of reports. You need some other products to build forms, complex reports, and manage special triggered code sequences. The base version of ORACLE (at least for our site) doesn't support object oriented programming. But you CAN buy the option that gives you such abilities.
Paradox is about like Access in what it supports. It uses forms, reports, and has code modules with event-based triggers. It, too, grants visibility to object properties.
ShareBase is an older product - probably not found very often - that ONLY supported SQL functions and acted as a back-end server for many front-end products to take care of forms, reports, and the like. Decidedly NOT object-oriented.
So if your question is just a general inquiry, then all of these answers (including mine) are direct answers that have some validity. But if you are looking for specifics, rephrase the question.