To make it easier for you I went to wiki and copy and pasted the different styles for you. I also listed some bands for each subgenre so that you might listen to them and see what the differences are.
Thrash - Thrash metal originated, and remains, NWOBHM[1][2][3] with tempos influenced more predominantly by hardcore punk. Thrash metal songs are usually fairly complex, and frequently contain constant time and tempo changes. Thrash metal replaces melody with brutality and speed, with the use of ample distortion. Thrash was the first subgenre to widely use double bass drums in metal. Vocals in thrash metal are usually yelled, screamed, or snarled, though, at the same time, melodic.
As is true for many of the terms in this list, the moniker "thrash metal" was not always embraced by its supposed representatives; early on, Metallica referred to themselves as "power metal" (conflicting with the above definition of this term). Conversely, many bands, like Kreator, have been labeled as hate metal.[4]
Examples of Bands: Metallica, Megadeth, Exodus, Slayer, Testament, Anthrax, Iced Earth, Trivium
Avant-garde Metal - generally regarded as a cross-genre reference to metal bands or more exactly as a stylistic adjunction with specific traits (just like Progressive-, Symphonic-, Viking-, Pagan-, Folk-, Industrial-, Post-). It is characterized by large amounts of experimentation and by non-standard sounds, instruments, and song structures. Has a general dark atmosphere to it.
Examples of Bands: Celtic Frost, Fleurety, Ved Buens Ende, Moonspell
Black Metal - an extreme metal subgenre. The genre is characterized by an aggressive and abrasive sound, coupled with a dark atmosphere. Black metal artists typically achieve this sound through the use of heavily-distorted guitars, harsh vocals, fast-paced rhythms, and unconventional song structures. An ideological rejection of Judeo-Christian values is often seen as central to black metal.
Examples of Bands: Bathory, Mercyful Fate, Hellhammer, Celtic Frost, Venom, Cradle of Filth, Dimmu Borgir
Classic Metal - Classic metal is a term used to refer to heavy metal bands from the 1970s and 1980s who peaked later than the late 1960s and early 1970s pioneers of the genre, yet before the era when mainstream and underground heavy metal became seriously divided. Classic metal bands are typically characterised by thumping fast basslines, not so fast, heavy but "clean", riffs, extended lead guitar solos, high pitched vocals and anthemic choruses. Classic metal is related to such genres as glam metal, hard rock and the New Wave of British Heavy Metal, and sometimes overlaps with these genres.
Examples of Bands: Accept, Black Sabbath, Blue Oyster Cult, Alice Cooper, Def Leppard, Dio, Ozzy Osbourne, Queen, Queensryche, Deep Purple
Death Metal - brutal extremes, with dissonant harmonies, exotic scales, erratic time signature changes and downtuned guitars. Double bass drums are universally implemented, as well as rapid snare drums, 'blast beats', and chaotic cymbal crashes. Vocals are usually growled, but also can be shrieked, yelled, or screamed. Current death metal bands often dabble in neo-classicism, Jazz-fusion, medieval music, or folk and symphonic endeavors. The lyrical content usually deals with the darker, nihilistic side of human imagination, dealing with blood, death, gore, and Satan (like the band Deicide). However, Death Metal is not limited to just blood, death, and gore. It can also range out to philosophy, Mythology (such as the band Nile), and politics.
Examples of Bands - Amon Amarth, Cannibal Corpse, Death
Doom Metal - The subgenre of doom metal differs from others in many ways. Instead of fast paces, pure doom metal uses only mid or slow tempos; the atmosphere emphasizes melancholy feelings. Candlemass is one of the most important bands of the genre and their first album, Epicus Doomicus Metallicus named and defined the genre. Some bands, such as My Dying Bride and Bethlehem, mix death metal or black metal with doom metal using the vocals from death or black and the tempos of doom. Doom metal often uses three octave major scales played on the 7th fret for riffs as well as solos. Several strains of doom also maintain heavy influence from the originators of heavy metal such as Black Sabbath and Deep Purple.
Examples of Bands: Burning Witch, Candlemass, My Dying Bride
Folk Metal = Folk metal embraces metal bands that are influenced by folklore from varying cultures and origins. Originally started as a mixture of folk rock, power metal and black metal, the term has progressed to encompass many folk-themed metal bands, that use folk based lyrical themes and composition, including instrumentation
Exmamples of Bands: Finntroll, Mägo de Oz, In Extremo, and Skyclad.
Glam Metal - Glam metal was one of the most popular styles of metal during the 1980s, often referred to by detractors as "Hair metal". The sound; as the name suggests lies somewhere between the Heavy Metal sound of Black Sabbath, Deep Purple and the Glam rock sound of Sweet and KISS. The bands were famous for their use of guitar solos, energetic frontmen and drummers that did not only have technical ability, but the ability to put on an entertaining show; as per Tommy Lee. Many of the bands donned make-up to achieve an androgynous look, similar to that of some 1970s Glam rock bands.
Examples of Bands: Twisted Sister, Motley Crue, W.A.S.P, Quiet Riot
Gothic Metal - Gothic metal is a genre of heavy metal music that originated during the early 1990s in Europe as an outgrowth of doom-death, a subgenre of doom metal. Musically it combines the guitaring styles of doom metal, black metal and death metal with its own unique use of heavy keyboard atmospherics, romantic and story like lyrics and dual vocalists.
Examples of Bands: Within Temptation, Lacuna Coil
Grindcore - Grindcore is influenced by thrash metal, and also hardcore and punk, taking its name from the "grinding" sound made by the atonal riffs 'grinding' into one another. The style is characterised by a vocal style similar to death metal, rapid fire "blast beats" from double-kick drums and short songs. There are grindcore bands that are more hardcore than metal, but most bands today are heavily influenced by death metal. The heaviness of Grindcore is slightly comparable to the heaviness of death or black metal.
Exmples of Bands - Carcass, **** and Ball Torture, Pig Destroyer, or Napalm Death.
Industrial Metal - Industrial metal (also referred to as noise metal and cyber metal) fuses elements of industrial music and other electronic genres such as House music by using electronic instruments such as Synthesizers and drum machines alongside more purely heavy metal instruments such as Guitars and Bass and a vocal style combining elements of both genres.
Examples of Bands - Tool, Rammstein, Fear Factory
Metalcore - Metalcore is defined usually by bands whose music combines both the raw vocals and beat of American hardcore (generally within the Northeast US) with the guitars more often used in European thrash metal and melodic death metal.
Band Examples: Killswitch Engage, Shadows Fall, Atreyu, Haste the Day, and Avenged Sevenfold.
Neo-classical metal - Neo-classical metal incorporates elements from classical music, into the normal heavy metal sound, including tempos, instrument usage, and even melodies.
Band Example: Yngwie J. Malmsteen
Nu Metal - Nu metal is a style that combines elements of heavy metal, hip hop and alternative rock music, with a downtuned guitar technique. There is some contention between metal fans, that, given nu metal's alternative rock ties, calling it a metal genre can be considered a misnomer.
Band Examples: (hed) Planet Earth, Linkin Park, Slipknot, Korn, Deftones, Limp Bizkit and Coal Chamber.