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)
Yasuaki Yamauchi has written: 'Jinja kenchiku' -- subject(s): Architecture, Japanese, Japanese Architecture, Shrines
The cast of Jinja jinja johahae - 1977 includes: Hyeon Kim
神社 Jinja is Shinto shrine 寺 otera is Buddhist temple
Nagata jinja was created in 201.
Tokiwa Jinja was created in 1874.
Mikado-jinja was created in 718.
The population of Jinja District is 491,000.
Toga jinja was created in 701.
Masumida jinja was created in -628.
Olive Jinja was created in 1973.