It all boils down to semantics as gamma is in the video world often used to describe any kind of curve.
Technically gamma refers to the exponent (or the reciprocal value) of a function and defines how much a linear function is "pulled up or down".
For instance below is a graph with various gammas, starting with the red line which is x to the power of 1 thus a gamma of 1, then going upwards with a gamma of 2, 2.2, 2.4 and 2.6 (or the reciprocal values). So for instance x to the power of 0.45 is a gamma of 0.45 (or 1/0.45 = 2.22).
A log curve is something different and based on the log function, below is a graph with Rec709 (using a gamma of 2.22 or 0.45) and Panasonic's V-Log as an example.
By the way Rec709 is not a complete gamma curve as it is linear at the bottom.