Document Database
This is the most common database type. Handles all the information in documents.

If you are familiar with Relational Databases just think that documents are like records but without a schema, unless you want to define it. Relationships are made no with "joins" but are directed between documents. Documents are collected into clusters that are similar to the "tables" but can contain different types inside of them. A subset of SQL is supported with special powerful operators to simplify complex statements.

Graph Database
Use this if you want to handle all your data under the form of Vertices and Edges. To query the database a special SQL language is provided with operators to traverse the graphs in easy way.