There are different kinds of databases that are designed for different uses.
File Based Databases:
File based databases (like Ms Access or Filemaker) are designed to run on the user’s computer, or on a local network. They usually have development tools built into them and come with many wizards to help users do common tasks.
Server databases run as services and can be communicated with from applications that need to use their data. Good examples would be Ms SQL Server or MySQL. They are usually more complicated to set up and run than file based databases but offer more robustness, greater speed and stability. They are often used to supply data to websites.
NoSQL databases, like Couchdb or Mongo, are based on a document model rather than on a table model. Data is stored in documents, which can have fields that vary from document to document.