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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.
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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.
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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
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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