"Fat-Washing" is when a spirit is imparted with an oily/fatty character without making it greasy. To accomplish this, one might take a fatty cut of meat or fried chicken and soak in it the spirit for several hours. After allowing it to sit in a freezer to let the fat coagulate (I hate that word) , the liquid is strained through filter paper. The oils add intriguing flavors and textures to cocktails. Ummmm. YUCK. Does salmonella come to mind??? OK....maybe tequila kills bacteria, but still.
"Spherification" is the creation of tiny gelatinous (another creepy word) globes that have liquid inside them. The globes or "pearls" as they are sometimes called, can add flavor but are employed more for visual intrigue to cocktails or Champagne. This is for more advanced bartending situations where presentation is important........ Like WHERE would this be important?? It doesn't even make sense....and if a cocktail is too complicated to make sense....well, that says a lot.
I am obviously not a sophisticated cocktail drinker. Donna's "half and half" vodka and cranberry is more my style.