What is the difference between Philanthropy and Philanthropism?
Solution 1:
The OED defines "philanthropism" as
The profession or practice of philanthropy; a philanthropic theory or system.
This follows from meaning 2.A of "-ism":
Forming the name of a system of theory or practice, religious, ecclesiastical, philosophical, political, social, etc., sometimes founded on the name of its subject or object, sometimes on that of its founder
Sometimes there are not two different words (eg "catholicism" which can refer to an individual's belief or practice, or to the movement), but in this case there are two. Similarly we can distinguish "anarchy" from "anarchism".
So in your particular case, either is possible, but they will have slightly different meanings: "philanthropy" would focus on the individual people (or acts) that are philanthropic; "philanthropism" would focus on the system or theory or philosophy of philanthropy (if there is one).
Solution 2:
Philanthropy is the act of philanthropy itself.
Philanthropism is characteristic of philanthropy, the system.
It's made a little more clear if we consider other words, such as alcohol or communist:
He suffered from alcohol.
He suffered from alcoholism.
The communist got to him.
The communism got to him.
The -ism suffix comes from the Latin ismus to indicate a state or condition.