It is not uncommon for the term non-denominational to be used where the term inter-denominational should have been used. At fist glance, there may not appear to be much difference between these two terms; however, upon closer examination, it will become evident that these two terms are almost antonymic.
Inter-denominational is the easier term to define. It describes an organisation or activity that includes members of different Christian denominations. For the sake of the organisation or activity, doctrinal differences are ignored and common ground is emphasised. Such organisations or activities are ecumenical.
The definition of non-denominational is not so concrete, but more theoretical. It is the absence of denominations. Truthfully, an organisation that claims to be non-denominational is really deceiving itself, being really just another denomination.
I may be mistaken, but I believe that it was Barton Stone, very early in the 19th century, that first used the term non-denominational. Stone believed that Christians could unite in one faith, and do away with the division within Christianity, which was termed denominationalism. Stone's attempt to accomplish this failed, and he abandoned all established churches to form a new church simply calling themselves Christian. Stone soon joined with Alexander Campbell in what is commonly called the Restoration Movement, in which Stone's idea of non-denominationalism became quite dominant.
This endeavour to be non-denominational is a noble one, and is actually an attempt to bring the same unity that is found in the Catholic Church to Protestantism. However, without a governing body to maintain orthodoxy, Protestants cannot unite. The Restorationists have an even more difficult time maintaining orthodoxy because of their additional doctrine of congregational autonomy. Despite their attempt to restore Protestantism to first century Christianity, Restorationists have only succeeded in creating more denominations.
The Catholic Church has a governing body to maintain orthodoxy: the papacy. It was in rebellion against this authority that denominationalism came to be. The only solution to denominationalism is not in more rebellion, but in submission to the Christly ordained authority of the pope.
Inter-denominational organisations and activities are good since they unite Christians. All groups that claim to be non-denominational, however, do not unit Christians, but created further division. True non-denominationalism in Christianity really only exists in one place, the Catholic Church; although she doesn't uses this term. The churches that do use this term are really only perpetuating denominationalism.