Technology is a specific application of a methodology (whether the methodology is known or understood or not). Bronze age people discovered that when arsenic or tin was added to copper, it made it much harder, but they had no idea why that was so; the methodology came five thousand years later with the understanding of how small amounts of impurities “lock up” layers of atoms so that they don't slip and deform when shearing force is applied to them.
A methodology is a more general understanding of how things work, in contrast to a specific recipe or product. Richard Bandler has often said that “NLP is a methodology that leaves behind it a trail of techniques.” Most NLP trainings include a mixture of methodology and technology. Specific techniques (e.g. phobia procedure, change personal history) are taught along with at least part of the methodology (e.g. rep. systems, submodalities, anchoring) that underlie the specific techniques.
Knowledge of methodology allows the user of technology to adapt it to unique situations in which knowledge of the technique alone would fail. Methodology also makes possible new applications and discoveries, and new ways of accomplishing outcomes that we already have techniques for.
For example, an engineer who understands the methodology of materials and structures can build a specified building out of a wide variety of materials, utilizing a wide range of structural elements, and predict with mathematical models exactly what size to make everything to achieve a certain strength to resist hazards such as snow load, flood, earthquakes, etc. In contrast, if the same engineer only knew about how to build brick walls, he would only be able to design a narrow range of buildings for a few environments.