In terms of meaning there is no real difference, they both translate as 'shrine'.
However, Jinja is just a general term for any shrine, whereas Jingu denotes a more prestigious establishment, usually linked to the Imperial Household (Japan's equivalent of a Royal Family) or enshrining an Emperor.
There are lots of other words for shrine: Yashiro, Miya, Hokura, Taisha... all indicating slight differences in function and status.
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It is 'jinja' in Japanese. (Japanese: 神社)
a Shinto shrine is called a "神社" (Jinja)
The cast of Jinja jinja johahae - 1977 includes: Hyeon Kim
Yasuaki Yamauchi has written: 'Jinja kenchiku' -- subject(s): Architecture, Japanese, Japanese Architecture, Shrines
神社 Jinja is Shinto shrine 寺 otera is Buddhist temple
Saruka Jinja was created in 807.
Terukuni jinja was created in 1882.
Ebetsu Jinja was created in 1915.
Tokiwa Jinja was created in 1874.
The population of Jinja District is 491,000.
Futarasan jinja was created in 767.
Senkaku Jinja was created in 2000.