Just about every "JPEG image" that you encounter will be in either JFIF or EXIF file format. These two file formats are virtually identical in terms of encoding – except for the different "header" (or "Application Segment"). If you have software that handles JFIF files, then provided that it isn't strict about requiring a JFIF header, it should be able to handle most EXIF files as well.

One good example of an EXIF file that isn't in JFIF format is an image in CMYK color format. Such files are commonly used in the publishing industry. The four color channels C, M, Y and K are fundamentally different to the three channels Y, Cb and Cr within JFIF files.

For many years, browsers couldn't even display such CMYK JPEG files. Testing this today, I see that Firefox and Chrome both handle them okay – albeit with unnatural looking colors.

In summary, don't expect that software that handles JFIF files will automatically handle all flavors of JPEG files.