Is difference amplifier a differential amplifier with a voltage gain of one?
There is " no difference " between the terms "Difference Amplifier" and "Differential Amplifier"   (pun intended)


They both amplify the difference between 2 nodes, whether you have a signal on both or just one and connect the other one to some DC reference voltage. 

Then the impedance ratio is 50% going into the non-inverting side with a gain of 1/2*2=1, it is unity gain while the inverting side has the same divider ratio with a gain of -1 then it is a "unity-gain differential (or difference) amplifier" which is a special case of any "diff amp".( slang description = diffy)

Other info;

The gain and frequency shape can be varied as long as the ratios are matched. So instead of simply Rf/Rin=gain it can be any combination of RLC parts matched on both sides.  

Matching is the hard part for discrete parts (0.1% error on 4 parts &lt; 55 dB CMRR while integrated INstrument Amps (INA) offer  CMRR > 110 dB needing only 1 R shared to control gain instead of matching 4 parts or 2 ratios, using laser trimmed internal R's.