Wizards has fairly recently released character themes for D&D 4th Edition.
What is the difference between themes and backgrounds?
Can you pick one of each or do you have to choose between the two?
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Themes and background benefits, though both usually related to a character's background, are separate mechanical elements.
Themes usually give a character a class feature and/or a power for free at level 1, and then give additional power options that character can pick while leveling up instead of a class power. With the exception of Dark Sun themes, themes also provide a character with an additional class feature at level 5 and at level 10.
A background benefit usually has two skills associated to them and sometimes a language, and a character can choose one of those skills and either add it to their class skill list, or add a +2 bonus to skill checks with it or add that language to the character's languages known. The Forgotten Realms Campaign Guide has background benefits that give the equivalent of a class feature instead of the skill choices entirely.
Sometimes themes also have a mechanical background benefit tied to it, depending on the source of the theme. The themes that appear in the Neverwinter Campaign Setting have a background entry attached to them with the same name; as I don't have the book right to which to refer, I can't say whether you're required to choose that background or not.
Otherwise, your character's theme and your character's background benefit are picked separately.