Is there a difference or is it just terminology?
Many people consider that an "oriented graph" is what you get from a simple undirected graph when you assign a direction to each edge. The difference between that and "directed graph" is that a directed graph can have cycles of length 2 even if it is qualified as "simple", whereas an "oriented graph" cannot. On the other hand, there are zillions of papers that use "oriented graph" with identical meaning to "directed graph".
Applying these meanings pedantically in the negative doesn't seem to be a good idea. I'd be very surprised to see anyone using "non-oriented" of a digraph to imply that it doesn't have 2-cycles. I only recall "non-oriented" meaning that the edges don't have directions, which is the same as "undirected".