Art songs are songs created for performance in their own right, and are frequently called "popular" songs, although this term is generally reserved for more contemporary compositions. Generally they are defined as having an identified author(s). Art songs feature in many cultures.
Folk songs are songs of anonymous origin that are transmitted orally. They are frequently a major aspect of national or cultural identity. Art songs often become folk songs when people forget who the author was. Folk songs are also frequently transmitted nonorally, especially in the modern era.
Lots more coming....
Song forms (haven't decided if these should be separate pages yet)
Aria and recitative (Opera)
Chanson
Ballad
Hymn
Mass
Oratorio
Spiritual
Carol
Lieder
Pibroch
Gregorian Chant and plainsong
Rock and Pop songs
Cantata
Madrigal
Ethnic or indigenous songs (a horrible term to use but I couldn't think of an alternative just yet. Aboriginal song is the only area I have any expertise on)