No, image/jpg is not the same as image/jpeg, only image/jpeg is recognised as the actual mime type for JPEG files.
See https://tools.ietf.org/html/rfc3745, https://www.w3.org/Graphics/JPEG/ .
Serving the incorrect Content-Type of image/jpg to IE can cause issues, see http://www.bennadel.com/blog/2609-internet-explorer-aborts-images-with-the-wrong-mime-type.htm.