What is the difference between inner-denomination and non-denominations beliefs?

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.