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I have two series of photos shot on my iphone 6s on 10.3.2. The first series is in the regular frame, and the second series is in the "square" frame. I'm using exiftool 11.01 on macOS 10.11.6.

From the command line, when I run exiftool -a -G0:1 on photos from the first series, I get: [Composite] Field Of View : 63.7 deg And when I run the same on the second series, I get: [Composite] Field Of View : 49.6 deg

Both of these reported values differ significantly from all of Apple's official technical specs for the camera, seen here.

Can someone please clarify the discrepancy, and indicate which FOV value I should use when asked for the "angular field of view," i.e., the total opening angle of the camera lens?

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In the linked tables, FOV refers to horizontal field of view, according to the key. The discrepancy would be due to the fact that the values calculated by exiftool refer to diagonal angle of view.

As pointed out in comments, "field of view" would technically be defined as a distance across a plane at a given distance from the sensor. In practice, "field of view" is commonly used to mean "angle of view", as in both of your sources. Angle of view is generally given as diagonal, unless stated otherwise, since this is the angle needed for a lenses image circle to cover the entire sensor. Therefore, when asked for "angular field of view", this is probably what's being asked for, but if it's important you should confirm this.

Note that the values given by exiftool are based on the reported sensor dimensions and lens focal length, and may or may not be accurate enough for any given purpose. The documentation you linked to seems to imply that the use of OIS can slightly alter the actual FoV, for instance. For any critical purpose you could do some empirical testing, either by measuring a physical scene, or using software such as Hugin to stitch a 360-degree panorama (it will calculate this information about the provided images in the process).

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    if you add a link to documentation for exiftool that shows FOV is for the diagonal measure, i'll accept your answer.
    – grad student
    Jun 24, 2018 at 4:23
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    Using the diagonal as the primary measure of a lens' angle of view has been the standard for at least a century before EXIF ever existed. In the absence of a description to the contrary, a single AoV value is always assumed to be measured diagonally. This diagonal measure also corresponds to measuring the diameter of the lens' usable imaging circle (assuming the lens is designed for the particular format size of the film or sensor in question).
    – Michael C
    Jun 24, 2018 at 7:40
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    Also note that apple's description as "field of view" (FoV) when expressing an angle of view (AoV) is incorrect. If the expressed value is an angle, it is an AoV and not an FoV. An FoV is expressed in a linear measure that is perpendicular to the optical axis at a specified distance from the camera/binoculars/telescope/etc. As in, "FoV = 176 feet @ 1,000 feet."
    – Michael C
    Jun 24, 2018 at 7:46
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    You can find the appropriate code that exiftool uses to make the Field of View calculations here. There is a note that it references Field of View - Rectilinear and Fishye Lenses on BobAtkins.com.
    – StarGeek
    Jun 24, 2018 at 15:43
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    Further searching through the code, it appears that it calculates ScaleFactor35efl on the diagonal. Those calculations can be found in the CalcScaleFactor35efl subroutine.
    – StarGeek
    Jun 24, 2018 at 15:53

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