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?
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.