I think in the context of this thread, a "Muslim country" is one that is full of Muslims. Malaysia is a Muslim country because the majority of the population are Muslims. It is not an Islamic country, in the eyes of many people, because Sharia is not enforced as some Muslims would like. An Islamic country refers to the ideal - which does not exist and probably has not since the 7th century and probably never will in my opinion - a Muslim country refers to the reality.
Ya and I think the same can be said about Lebanon. 75% are Muslims yet it does not implement any Sharia laws. Of course the president is Christian so I wouldnt expect it.