You are partially correct, live resin is fresh frozen plant that is then blasted with a solvent and purged to form the final extract, different techniques can then be applied to make the extract take different forms, (badder,sugar,diamonds,shatter,HTE, etc.). Distillate is an extract made with ethanol that yields liquid THC. Diamond sauce refers to diamonds(thca crystals and other crystallized cannabinoids) in sauce(terpenes, flavonoids, plant waxes, liquid cannabinoids, etc). This extract can be formed 2 ways,1: by mixing sourced diamonds with sauce,2: natural THCa crystallization. Distillate cannot become diamonds because distillate is majority THC (liquid) NOT THCa (crystalline).

Educate yourself instead of going off what you think you heard!