ARDS is widespread inflammation of the alveoli, so with that in mind, you get opening of the post-capillary venule by the various inflammatory mediators (eg PGI/E/D, leukotrienes, etc etc). That causes fluid to fill the alveoli spaces and with that fluid comes inflammatory cells, namely neutrophils. Since plasma is being leaked into the space wholesale and neutrophils are coming into the space, the fluid that accumulates is high in protein and high in cells. That classifies it as an exudate.
In contrast, a transudate is basically plasma being filtered through tiny pores in the capillaries. Since cells are too large to fit through the pores, the fluid is low in cellular matter. Since proteins are either charged or too large to fit through the pores, the fluid is low in protein as well. That classifies it as a transudate. Typically, anything that pulls fluid preferentially or push fluid preferentially will lead to a transudate. In left CHF, blood is backed up in the left atrium, which backs blood up into the pulmonary circuit. That increases the pulmonary circuit pressure, causing fluid to be filtered against the capillary. The most common cause of RHF is LHF, so that's how a transudate will be associated with RHF. In cases of cor pulmonale, where the RH fails independently of the LH, then fluid is backed into the systemic circuit and this is where you get pitting edema. This occurs in the leg because you have gravity acting on the fluid as well as the excess fluid being backed up, causing a transudate to flow out of the circulation. Finally, if there is an imbalance between capillary and interstitial oncotic pressure, this will force fluid to leave the circulation and into the interstitum, which leaves behind enough oncotic pressure in the capillaries to balance out the disparity. Since protein and cell-free fluid is accumulating in the interstitium, this fluid is also a transudate.
