Think of glossy as of a diffuse base material with a glossy coating. If you set glossy's specularity and exponent to 0, it will become a matte (although will be computed much longer, as will still has to take into account the invisible coating).
Shinymetal is a metal based model. Metals doesn't exhibit diffuse properties, and don't mostly have their own color, it's taken from what is reflected in the metal object. Thereby, glossy and shinymetal are two completely different models, you can't substitute one with another.
Mirror, yes, it's a shortcut for shinymetal with 0 specularity (don't forget, in real life mirrors are also made of a thin metallic layer on the back of a glass). It should work slightly faster than shinymetal though.
On the same kind of topic, is there any difference between the Light material and Matte with emission enabled?
If you're asking like that, then there is no difference. However using a specific material (other than a default matte with 0.8 reflectivity) with emission component is useful in two cases: First, when the emission is very low, so you can see the base material through it. Second, if you're going to use lightgroups -- when the lightgroup is disabled, an emissive object will show its base material. The "light" material itself has a matte as its dummy base.