Let me begin by saying that, there are several kinds of Japanese poetry forms and form names. It may, at first pass, seem rather confusing, but most of these poetry forms are very specific and not in common usage (though the internet has plenty of information about them, to suss out, if so inclined).
Today, the two major forms of Japanese poetry in western poetry are haiku and tanka. Both forms are very popular and both forms are never referred to in the plural.
Haiku originated in the 17th century. Haiku are a short, 3-line verse form. The first line has 5 syllables (which are referred to as morae). The second line has 7 morae. And the third line has 5 morae. The 5/7/5 rule for haiku in English is just an approximation of the rule for traditional Japanese haiku (as worldwide translation makes this impossible to maintain).
Haiku is built on the juxtaposition of two images or ideas. In the past, these were nature based, but, more and more, it is felt that these images or ideas should be directly observed everyday objects or occurrences. Other traditional features, it seems to me, have become more flexible and are not always employed. (These include: a cutting word that cuts the stream of thought between the two images or thoughts – and a seasonal reference or observation.) When haiku is added to a Japanese painting (in the traditional manner), or ink drawing or photograph, it is called a haiga. When a haiku is added to a short prose piece – by way of enhancing or completing (and not simply repeating) the idea, it is called a haibun. A senyru is a 3-line unrhymed Japanese poem, that is similar, structurally, to haiku, but treats human nature in an ironic or satiric way.
Tanka originated over 13 centuries ago. Tanka are a short, 5-line verse form. Traditionally, the first line has 5 syllables (morae). The second line has 7 morae. The third line has 5 morae. And the fourth and fifth lines have 7 morae each: as in 5-7-5-7-7. However, as with haiku, this is just an approximation. In general (though not always) tanka speaks to a personal experience and the resulting deep feeling. A good way to approach writing a tanka is to begin with the first two lines speaking to an experience of the poet (an observation, a feeling, a sense). The third line (called the pivot) should change the tone of the poem. It should relate separately to the two lines above and the two lines below. The final two lines should express reflection or even, transcendence.
Worldwide, tanka has a huge following. If the number of tanka journals, are any indication, I suspect its popularity surpasses haiku. I have read many poets' thoughts on why they love writing tanka. There are many, many reasons. I can only speak to my own. Tanka allows me to write down a truth ... relatively expeditiously – but thoughtfully. It captures moments of life and relationships and communion with nature. It helps me to see the world clearer. It's fun ... it draws you in. And, as I've said – more than once – it's my ''go-to' place, when I don't know what to do with myself.