Heavy Metal @ Wikipedia wrote:
Heavy metal is typically characterized by a distorted guitar-led sound, morbid themes and lyrics, straightfoward rhythms and classical or symphonic styles. However, heavy metal subgenres have their own stylistic variations on the original form that often omit many of these characteristics.
According to Allmusic.com, "Of all rock & roll's myriad forms, heavy metal is the most extreme in terms of volume, machismo, and theatricality. There are numerous stylistic variations on heavy metal's core sound, but they're all tied together by a reliance on loud, distorted guitars (usually playing repeated riffs) and simple, pounding rhythms."
Goth Metal @ Wikipedia wrote:
Lyrically, gothic metal is centered around romances and fantasy tales that end in tragedy for one or more parties involved. The setting for the lyrics are most often in the New Age or the Dark Ages, but can also be in Victorian, Edwardian, Roman, or modern eras. The romantic- and fantasy-themed lyrics often used in gothic metal cover many broad subjects and are intended as being themes and guides to the lyricist, rather than a complete prerequisite of the genre. Gothic Metal bands typically do not write their albums in the form of separate songs; they rather write concept albums in the form of books. This is so that each song acts as a part, or, chapter, inspiring people to listen to the whole album in order to hear the story, instead of just certain songs. Penumbra's Seclusion and Silentium's Sufferion - Hamartia of Prudence are two gothic metal albums that feature this style of lyrics.
I've never heard of Fantasy Metal. It's probably similiar to Gothic Metal.
Black Metal @ Wikipedia wrote:
Black metal may, but is not obliged to, have the following characteristics:
* Fast guitars with tremolo picking
* Lyrics that take the form of pessimistic, Satanic, Pagan, or occult themes which blaspheme Christianity. Bands such as Slayer, Deicide, and Immolation overlap lyrically with black metal somewhat but are musically defined as death metal (Immolation, Deicide) or thrash metal (Slayer)
* Relatively thin guitar sound or relatively thick guitar sound, usually not in the middle.
* Limited production used intentionally as a statement against mainstream music and/or to reflect the mood of the music, to create atmosphere. This 'underproduced' effect is often achieved by cutting out low and high frequencies, leaving just the mid frequency range. Very few of the black metal pioneers still do this, since their original limited production only was due to a minimal budget. This production style is often considered an essential element of "true" Black Metal.
* Fast, repetitive, aggressive drums, often with blast beats. At other times, the drums can take a slower role usually accompanied by a very dry and empty tone —especially for the effect of the atmosphere of the music.
* Occasional electronic keyboard use. The harpsichord, violin, organ, and choir settings are most common, which gives the music an orchestral feel or a cathedral-like setting. Some bands tend to use keyboards very frequently, whether it be as an instrument or even as the basis of their entire sound. They are generally placed under the symphonic black metal label.
* High-pitched/distorted screeching vocals. Contrary to popular belief, these are not essential as there have been many black metal bands old and new employing different vocal styles.
* Swift percussion.
* Cold, dark, sad, melancholy, or gloomy atmosphere.
* Less focus on dynamic rhythm than death metal. Very few black metal bands exhibit the rhythmic complexity inherent in death metal, and even if they do, they usually exhibit at least a few of the above-listed criteria if they are still generally classified as black metal.