As you can see in the graph (above), standard Rec. 709 has a limited dynamic range; add a knee point, and you get more. Hyper-gammas and Log modes push it even further. The results on a monitor can be seen in the second image (below).
The images with more range tend to look better to us, and certainly allow for more adjustment in post, but don’t conform specifically to a Rec. 709 standard. These higher-range modes vary from camera to camera, but most can produce images that are "legal" for Rec. 709 displays—meaning that the video signal levels are in that 0-100% range on a waveform. Many cameras have a Rec. 709 gamma mode, which usually aims to be close to that standard with limited range. But, it turns out that even those modes vary from camera to camera based on the sensor, and whatever the camera manufacturer thinks produces the best result.
In other words, monitors conform to the gamma standards of Rec. 709, but cameras generally do not. This is a big reason why setting two cameras to Rec. 709 mode doesn’t guarantee they will look the same. Different gamma means different contrast and dynamic range. Contrast is just half the equation, of course; the other half is color.
RUN THE GAMUT
Rec. 709 has a specific requirement for color gamut and white point. It specifies the utmost red, blue and green values that can be shown on a monitor, and a white point of D6500. The RGB primaries define the gamut of Rec. 709, which you can see above outlined over the CIE chart (human visible color chart). All Rec. 709 monitors are meant to conform to this gamut and white point. This standard helps guarantee that what we see from monitor to monitor will be the same. Of course, consumer televisions can vary, but a calibrated Rec. 709 monitor aims to get the white point and primaries correct.