Cantonese and Taiwanese are part of Chinese dialects,people from Guangdong province and Hong Kong speak Cantonese,people from Taiwan province speak Taiwanese,but I think people from these regions could also speak Chinese now.There are also many other dialects in China,such as Goetian (a dialect that is spoken in Suzhou,east of China),Shanghai dialect,Beijing dialect.Beijing dialect is similar with Chinese.In China,many northern dialects are similar with Chinese,but southern dialects are not,people from south China could undertand northern dialects,but north Chinese may not understand south dialects well.Mandarin is the official name of Chinese,I think there is no exact difference between Mandarin and Chinese.There is also an opinion that Mandarin is the old name for Chinese,I think Chinese may more modern than Mandarin.