Delphi Technique, ideas are gathered from group members (who are experts and can be anywhere in the world) but there is no communication between participants. These ideas are compiled and the most common are put forward for further comment by the group members. Multiple rounds can follow with the intent to reach as much a consensus as possible. This could be a protracted process depending on the number of rounds necessary to achieve some consensus. Therefore, it would not be amenable for situations where predictions are needed for short-term decision-making.
In contrast, Nominal Group Technique (NGT) involves face-to-face meeting and opinions are given which allows for direct interaction. The structure involves members working by themselves and contributing their initial thoughts. There is then a period where members can discuss and after that members split off again to finalize their individual conclusions. The majority consensus would be drawn from these final individual work efforts. This type of approach is particularly amenable to specific problem solving that cannot afford long protracted rounds of deliberation. Both techniques use contributions from experts but there is opportunity to discuss face to face in NGT.
One example for using NGT would be for problem solving using a small group of experts where the problem is narrowly focused and consensus needs to be achieved within a short time (Graefe, & Armstrong, 2011). In my job, one example would be a team with representatives from different agencies. The team is charged with coming up with best practices for a future technology initiative that is imminent. There is no time for many iterations and involves a motivated group of experts. They would be able to identify top priorities in best practices through the NGT method.
Graefe, A., & Armstrong, J. S. (2011). Comparing face-to-face meetings, nominal groups, Delphi and prediction markets on an estimation task. International Journal of Forecasting, 27(1), 183-195.