Chinese refers not only to Mandarin Chinese, or ‘Pu Tong Hua’ (translatable as “the common language”), but also to what we call “dialects” that include Cantonese, Hokkien, Hakka, and Teochew.
We call them “dialects”, but they’re distinct enough from Mandarin Chinese that they can be considered their own languages. For example, the difference between Hokkien and Mandarin is similar to the difference between German and English.