Unlike Chinese calligraphy, Japanese calligraphy utilises several different writing systems. Those are: kanji (漢字), katakana (片仮名), and hiragana (平仮名) the writing systems known to anyone who studies modern Japanese language, but also hentaigana (変体仮名), manyōgana (万葉仮名), and so on.
To understand the history of Japanese calligraphy, it is best if you read my article on the subject. However, for the sake of better understanding of this article, it is necessary to say a few more words in regards to those writing systems.
Japanese kanji evolved from Chinese characters. Since Japanese grammar is completely different from the Chinese one, there was a need for developing a writing system to be used for distinguishing prefixes, grammatical expressions, etc. Today, hiragana syllabary is used for dealing with grammatical issues, and katakana is mostly used for writing foreign names and as phonetic explanatory notes.
Historically speaking, various different types of Japanese calligraphy have evolved, depending on which writing system, or writing systems, are applied in a single calligraphy work. For instance, the calligraphy you see in the picture (above), is a typical kana majiri bun (仮名交じり文), which stands for: "a text that is a mixture of kana and kanji".
Another type would be chōwatai (調和体), which stands for "harmony of scripts". Such calligraphy can include both kana syllabaries and kanji, similarly to kana majiri bun, but the forms of characters or syllabopgrams are based on those found in classical literature. In this respect kana majiri bun is a modern form of chōwatai.
Last but not least, there is also kana script (かな), which refers to calligraphy written exclusively in hiragana and / or hentaigana.
Pictured calligraphy: 果てしない夏（の）愛 (everlasting summer love)
Ponte Ryuurui (品天龍涙)