NAM is Neural Amp Modeler. It is free software online that captures tones and uses machine modeling to make clones of the sound. Said to be the most accurate capture process currently. ToneX is based on a similar process.
Neural Quad Cortex is totally different.
I thought your Synergy tones were great and was surprised you didn't keep it. Great way to have some different tones to switch between when you get bored.