The Artistic algorithm is the original text-to-image AI art algorithm. Its' technical name is "VQGAN+CLIP". The artistic algorithm is great at producing beautiful textures and scenery based on descriptive keywords (modifiers), however the images often don't seem to "obey the laws of physics". For example, it's common to see a building floating in the sky, or a repeating pattern throughout the image.
The Coherent algorithm is a newer addition to NightCafe, and specialises in creating images that actually obey the laws of physics (usually). The coherent algorithm can be a little more hit-and-miss than the artistic algorithm, however most of the top artists on NightCafe prefer the coherent algorithm. The technical name for the coherent algorithm is "CLIP-Guided Diffusion".
The Stable algorithm is one of the latest additions to NightCafe and is even more coherent than the "Coherent" algorithm. "Stable" is short for "Stable Diffusion" - an open-source algorithm and model inspired by DALL-E 2, Imagen and other advanced systems.
The DALL·E 2 algorithm is an evolution of the original DALL-E by OpenAI. DALL-E kicked off the whole text-to-image scene by demonstrating that it was possible. DALL-E 2 brings a whole new level of coherence, resolution, and prompt accuracy.
Tip: you can get some great results by evolving an artistic creation using the coherent algorithm, or vice-versa.
See Acknowledgements for algorithm credits.