The principal difference among mic types is whether its transducer (the element for converting sound waves to electrical ones) is a dynamic or a condenser.
A dynamic mic works sort of like a speaker in reverse: A coil of wire is mounted on a diaphragm, which sits inside a magnetic field. When the diaphragm moves — reacting to the sound that’s hitting it — the fluctuations in the magnetic field that result create a current, which runs down the wire and into the board. A dynamic is the most widely used and economical type of mic. Found on performing stages everywhere, it’s also used extensively in the studio.
The SM57 and SM58 are two of the most popular dynamic microphones used for vocals and instruments. Dynamic mics are rugged and can handle high SPLs (sound pressure levels), like those delivered by kick drums, snare drums, and the speakers of cranked-up guitar amplifiers. They don’t pick up a tremendous amount of high-end detail, but this can be good, as they tend to reject rattles in drum hardware and guitar-amp cabinets.
A condenser mic uses a different method for producing signals than a dynamic model, and requires a constant electrical charge in the pickup element. The mic draws this power from an external source, such as a battery, a phantom power supply in a mixer, or an outboard mic preamp with built-in phantom power circuitry. Condenser mics are more sensitive than dynamics. This is usually a good thing in microphones (despite the quality of dynamics to reject rattles), as it yields better results in aspects such as high frequency detail and transient response.
Transients are the initial attack noises of a note, and are quite short. Small diaphragms, like those found in the SM81, have less mass and therefore require less energy to move. These diaphragms are very responsive to the small, high energy frequencies produced by the plucked string of an acoustic guitar.
For the same reason, small-diaphragm condensers work well as overhead cymbal mics. What small-diaphragm mics are less good at is capturing warmth, and responding to complex or pronounced low-end frequencies. For sounds with those qualities as required for vocals, you’d usually want to use a large diaphragm condenser such as a Nuemann U87 or Rode NT1000.