'Mandarin' specifically means 普通话 or 汉语 Chinese means any Chinese language, so it can include 广东话 or 客家语 or any other dialect. Westerners have not been quite so brainwashed as the Chinese into thinking that 汉语 is the only true / universal Chinese. That is probably partly because a lot of the early Chinese settlers in the west were Cantonese / 广东人, and came over to the west before they were forced to learn 普通话.

'Chinese' refers to all Chinese dialects and languages like Cantonese, Mandarin, Shanghaihua etc.

There are many kinds of languages and dialects such as Cantonese, Mandarin, The Chaoshan Dialect，The Shanghai Dialect，The Hakka Dialect etc. in China,but the formal one is Mandarin.People always use it in social activities.If you really interested in it,I am glad to answer you.

Maybe Chinese includes Mandarin and Dialects.