FALSE. They use both.
680 nm light impacts chlorophyle b within FS II, which provides energy to water molecules, which convert into O2, H+ and electrons. Electrons jump from one molecule to another, and this electric energy is used to produce ATP. 700 nm light impacts chloropyle a within FS I and provides energy for the electrons to keep jumping, which is necessary to produce NADPH. This NADPH will be used later to produce glucose. Other colors can impact other colored molecules which are also within FSI or FSII but they are not chlorophyle. These molecules cannot react with electrones, they just pass their energy to the chlorophyle, so the chlorophyle “feels” like she’s receiving a larger amount of her kind of light.