Liver is a confusing because it is the color of the points (the dog's nose, eye rims, pads, and lips) not the actual coat color. Only when the points are brown or liver color will the dog be labled as "liver".
Liver colored dogs lack the black pigmentation of the skin. Their noses, pads on their feet and lips will be brown, but their hair may have a other coloring, from very light to deep chocolate and everything in between.
Liver can range from light red, orange, cream coloration to deep chocolate. So, you can have white-liver, cream colored-liver, a red-liver, or a chocolate liver.
Some Shih Tzu dogs may have green eyes with this coloring, but not always.
The liver color comes from a recessive gene and for it to show up in a puppy, both parents must carry the gene.
This Shih Tzu is liver colored. Notice that her nose, eye rims, and mouth are the typical of the liver color. The hair is often called chocolate but chocolate is not an offical AKC color.
Blue is another confusing color. A true blue Shih Tzu will have a blue nose, but can have other colors of hair. The hair looks more charcoal and is often hard to see, except in natural light. Sun light is the best way to observe this rare color.
So if you are contemplating the purchase of a true blue colored Shih Tzu, it is best to visit the breeder personally rather than depend on a photo on the internet.
Blue is considered to be a dilute from a genetics point of view. A dilution occurs when the pigment (either black or brown). When this occurs pigment is clumped differently and distrubuted irregularly. If the pigment is black, then the dilution will result in the blue color. If the pigment is brown, the color that will be produced is a silvery color called Isabella. AKC regonizes blue but does not list Isabella color as part of their standard.