Fairly minor correction, but photosynthesis is essentially the opposite of cellular respiration. Plants do respirate and release CO2, but their photosynthesis more than offsets their respiration.
It's exhalations really. Their BO would result mostly from bacteria that live on their surface. You exhale your metabolic byproduct of CO2, they exhale their O2. Just, instead of one centralized set of "lungs", their respiratory system is decentralized through the structure, kinda like a lobsters "brain" is. Kinda.
Plants "breathe" normally too, taking in oxygen, and producing CO2. Separately, they also take on CO2 and sunlight, and produce "food" and expel oxygen.
Since it's a by-product of their "eating"... It really is a fart, isn't it?