The long and short version is that they each use a different mechanism within the body to reduce inflammation. Orencia works to reduce the activation of T cells (one of the early warning parts of your immune system) and tries to interrupt the activation of other cells in the RA inflammation process.
Remicade, on the other hand (like most of the other anti RA meds out today) inhibits the TNF. TNF stands for tumor necrosis factor and is a cytokine (message carrying protein is an easy way to think of it) that helps regulate immune system function. TNF is responsible (in part) for inflammation and inhibiting inflammation by inhibiting TNF function seems to help with RA in some people,