Strictly speaking, there is only one type of haiku. This is the traditional Japanese form of the poem. In the West, particularly in the English-speaking world, there are other types. There are also love, refrigerator and chain versions of haiku in these areas.
An English haiku contains 17 syllables and is split into three lines with a 5-7-5 syllabic pattern. In English, the term haiku has also come to mean all Japanese poetic forms. Other related poetic forms include the renga, choka and tanka. Tanka are the simplest and most common form.
A tanka consists of a 5-7-5-7-7 syllabic pattern and can be about any topic. Choka are similar, but the alternating lines of five and seven syllables can be carried on as long as the poet wishes before finishing with two lines of seven. The renga is a collaborative poem which combines a large number of Japanese style stanzas.
The traditional form must contain a seasonal word known as a kigo and it must also contain a juxtaposition known as a kireji. For example, Basho’s poem about a frog: “An old pond / A frog jumps / Sound of water.” The pond is the kigo and the kireji or cut appears between the jumping frog and the sound of water.
Fewer English haiku contain kigo and kireji. These are often more akin to a Japanese poem known as a senryu, which also has a 5-7-5 formation. Senryu, in Japanese are not haiku.
The haibun is a mixture of haiku poems and prose. The piece can be about any topic, but usually includes plenty of references to nature and emotions. There are no rules about how long it must be and how many poems are included. There are also no rules about how the poems and prose are mixed up and arranged.
A refrigerator haiku is a poem written on a fridge magnet. Such poems can be about any topic. They can also refer to poems written using magnetic words. It is also a catchall term for a funny haiku such as: "Haiku are easy, but sometimes they don't make sense, refrigerator."
A haiku chain is a series of linked poems. These are found on many writing website forums and are more a source of fun than a serious art form. The first poem's last line becomes the first line of the next poem and so on.