Calligraphy
Japanese calligraphy is called shodō. It is written in a flowing style with a brush and ink. Shodō is more than just a way to write the language, though. It is a traditional art form.
Japanese writing
Heavily influenced by Chinese, Japanese is written in 3 distinct systems: kanji, hiragana, and katakana.
Hiragana and katakana are both alphabets made up a letters that represent different syllables. Hiragana is used for words that don't have a kanji representations for prepositions, and word ending (kind of like -ing, -ed, etc...). Katakana is mainly used to write foreign words, though has a few other uses.
Kanji is a set of characters borrowed from Chinese where each symbol has a meaning.