LINQ stands for language integrated query. It allows you to use "SQL style" query language directly within C# to extract information from data sources.
- That data source could be a SQL server database - this is Linq to SQL
- That data source could be an data context of entity framework objects - Linq to entities.
- That data source could be ADO.net data sets - Linq to Dataset.
That data source could also be an XML file - Linq to XML.
Or even just a Collection class of plain objects - Linq to Objects.
LINQ describes the querying technology, the rest of the name describes the source of the data being queried.
For a bit of extra background:
Datasets are ADO.net objects where data is loaded from a database into a .net Dataset and Linq can be used to query that data after it's loaded.
With Linq to SQL you define .net classes that map to the database and Linq-to-SQL takes care of loading the data from the SQL server database
And finally the Entity framework is a system where you can define a database and object mapping in XML, and can then use Linq to query the data that is loaded via this mapping.
And also
all of them are LINQ - Language Integrated Query - so they all share a lot of commonality. All these "dialects" basically allow you to do a query-style select of data, from various sources.
Linq-to-SQL is Microsoft's first attempt at an ORM - Object-Relational Mapper. It supports SQL Server only. It's a mapping technology to map SQL Server database tables to .NET objects.
Linq-to-Entities is the same idea, but using Entity Framework in the background, as the ORM - again from Microsoft, but supporting multiple database backends
Linq-to-DataSets is LINQ, but using is against the "old-style" ADO.NET 2.0 DataSets - in the times before ORM's from Microsoft, all you could do with ADO.NET was returning DataSets, DataTables etc., and Linq-to-DataSets queries those data stores for data. So in this case, you'd return a DataTable or DataSets (System.Data namespace) from a database backend, and then query those using the LINQ syntax