A database, as its name implies, is a set of data stored within a database. Generally, each distinct database is a different dataset (though to be strictly accurate, each user/schema within a database would be a different dataset).
The most obvious example is an Oracle database; whether it is spatial or non-spatial, it is treated the same way by FME.
Feature Types within Database Datasets
In a database dataset, each different table within the database is considered a feature type.
For example, an Oracle database called "resources" has tables called "users", "vehicles", and "equipment". The dataset, in this case is "resources", whereas the feature types are "users", "vehicles", and "equipment".