While a flat-file is simple and easy to create, it is not suitable for large amounts of data, and does not provide a good way of locating individual records. You might open a flat file in a word processor like Word or Notepad and use the search function to locate a name, but the word processor must search through each letter and word in the flat-file until it reaches the first match.
Some database systems are intended for larger amounts of data than others, they all share at least one feature: the storage of data in a structure with indexes for quick retrieval. Some databases are open source (sometimes referred to as 'free': MS SQL Server Express, Mysql,PostGreSql, IBM DB2 Express-C, Oracle Database Express Edition, SQL Lite, Firebird) and others are not (MS SQL Server, Oracle, IBM DB2, Sybase).
Here are two articles you might want to read: Five Ways Open Source Databases are Limited and Why Would You Use a Commercial Database Anyway?. This may a moot point if you purchase software that includes or requires you to use a commercial database.
Some database systems can be installed on workstations (such as Windows 7, 8, 10), but these operating systems limit the number of simultaneuous users, and their hardware is usually not as fast and powerful as a server.
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