Stocks can become sauces through flavour reinforcement, and a binding element that thickens the sauce.
Binding elements that can be used are a roux (1:1 flour to butter) this preparation is allows the flour to be cooked out on the stove. The second method is a Beurre mainé (1:1 flour to butter) mixed together uncooked. you could also use double cream, egg yolk etc..
The Mother Sauces:
An emulsion is a smooth dispersion of one liquid into another which don’t usually combine. Mayonnaise is an example of an emulsified sauce.