The terms "database" and "database management system" are typically used interchangeably despite the fact the two mean completely separate things. Additionally, both are important terms that those in the technology industry should clearly know how to distinct between, but it seems many people either don't or can't. Very quickly, below are definitions for the two vocabulary terms.
A database is a logically modeled cluster of information [data] that is typically stored on a computer or other type of hardware that is easily accessible in various ways.
A database management system is a computer program or other piece of software that allows one to access, interact with, and manipulate a database.
Additionally, there are many types of database management systems that exist in the world today. Historically, relational database management systems (RDBMS) are the most popular approach for managing data due to their accessibility and performance result capabilities. Examples of RDBMS's include the Amazon RDS, Oracle, and MySQL which all utilize Structured Query Language (SQL) to manipulate the different databases they interact with. All RDBMS's are ACID compliant and typically implement an OLTP system.
To combat the limitations of relational database management systems, NoSQL databases became more popular over the years. The term "NoSQL" was coined by Carlo Strozzi in 1998 as the term for his first database which didn't utilize SQL for managing data, hence the label "NoSQL." Examples of popular NoSQL databases include key-value pair databases, document databases, graph databases, and columnar databases, all of which while are similar in concept are different in theory, as there are advantages and disadvantages to using each in different scenarios.
As we continue to move forward in the technology world, we constantly search for the most optimal solution for all of our data needs. These optimal solutions begin with which database management system or systems we choose to utilize to solve our data-related problems. Some database management systems are more equipped for certain scenarios than others, and figuring out which type works best for you is essential when working with big data.