Maybe this will help.

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,

@Kayak8 explained the difference in how they work really well.

As far as concerns with patients with heart conditions, the only concern I’ve heard of while working has been a concern when administering the medications to patients with congestive heart failure due to the possibility of then having a fluid overload. That is because both medications are given as IV infusions and are given every 2–8 weeks or so (give or take depending on the patients condition and which of the two medications it is).

Orencia is approved for moderately to severely active rheumatoid arthritis patients who have had an inadequate response to one of the disease modifying drugs; Humira, Remicade and Enbrel, which in addition to the TNF antagonists include:•
Rheumatrex
Arava
Plaquenil
Azulfidine
Orencia blocks the signal in the blood that is necessary for T cells to due their damage. Orencia has shown only mild benefit when used alone so it is best prescribed with another DMARD such as methotrexate or others to achieve optimal results, this applies to Remicade also. The biggest difference is that Orencia is the youngest of the drugs so results are still questionable.
Personally I have tried them all. Humira is the only one that allows me a somewhat normal life, Remicade and Orencia made me violently ill (as in close to death)