It is an interesting question. In one of the definitions of each the other word is used. I think that the main difference is that one that interferes actively intervenes, or meddles, in the affairs of others, while that which intervenes is more or less just there.
I hope that helps.
interfere
(def. 3) To intervene or intrude in the affairs of others; meddle.
interfere
http://dictionary.reference.com/search?q=interfere
intervene
http://dictionary.reference.com/search?q=intervene





