While LINQ only plays a role in a small part of an O/RM (the query language aspect), Entity Framework is much more than an O/RM: it is Microsoft's next generation API for abstracting database access on the .NET platform.

The old ADO.NET abstracted communication between different database platforms and left it at that; it did not unify the languages or results in terms of SQL dialects, database structure and field types.

Entity Framework however does just that: it also abstracts this level of communication with databases with eSQL, which each database vendor can translate to from their own SQL dialect. The Entity Data Model (EDM) can be mapped to abstract, vendor-specific database models, yielding unified data models that can be queried with a unified query language (eSQL). However, EDM and eSQL are both still on the relational level.

O/RMs plug in on top of that. In addition to LINQ to SQL, Microsoft introduced another O/RM called LINQ to Entities with Entity Framework that maps CLR business entities to EDM entities and also translates LINQ queries in the CLR business model to eSQL. In other words, LINQ to Enitites provides an additional abstraction on top of the Entity Data Model.

How does Genome compare to LINQ to Entities?

We are currently working on a more thorough analysis of the significant differences between Entity Framework and Genome. In the meantime, please check out the technical review of Entity Framework from the lead architect of Genome.
There is also an article on the Genome team blog that gives a general view on Entity Framework and what value proposition Genome offers over it.