SWAT uses the module Qual2E (or a newer variant) to model nutrient processing by streams. My understanding is that, traditionally, in this model MINERAL_P is interpreted to be the inorganic, soluble P (SRP, or ortho-P, considered to be the same here). And, ORGANIC_P is considered be everything else -- principally particulate P, whether organic or inorganic. I'm skeptical, because I don't didn't find whether Qual2E explicitly modeled adsorption / desorption of P from mineral particles -- which one would think ought to be an important form of P in rivers.
In addition to MINERAL_P and ORGANIC_P, Qual2E also keeps track of chlorophyll -- which is from algae, and Qual2E assigns a P content to that algal load. So technically, this is another part of the P load.
However, when a reach delivers its load to a reservoir, the reservoir receives the MINERAL_P and ORGANIC_P load -- but I don't think it keeps track of the Chlorophyll load. I could be wrong here... but in general I would carefully track your output to test whether the model is correctly passing P between reaches and reservoirs.
Currently --- I just do not use the stream water-quality routines (Qual2E). In this configuration, the model keeps good track of P coming off the landscape and what gets routed downstream, both through the reaches and through the reservoirs (and what may be deposited in reservoir sediments).
-- Jim