Modern China calls its people 中華民族 which means, as far as I know, that they are people from 華夏 and they are succeeding history and tradition of 華夏.
Zhonghua 中華 ('the Civilized Centre') is a relatively old term to refer to the area occupied by Huaxia 華夏 ('the Great Civilization'), which is now known as 'China'. It first appears in texts of the Age of Fragmentation, Sui, and Tang.
Minzu 民族 (literally 'people-lineage') is a new term invented in the 19th century in Japan, and used to translate 'nation'. The Chinese borrowed it to translate a number of different but related terms: 'nation', 'race', and 'ethnic group'.
Zhonghua Minzu 中華民族 is a composite of the two terms, first used in 1902 by Liang Qichao to refer to what were then commonly known as the 'Han' people. This usage of Zhonghua Minzu as a synonym for the Han continued until the early Republican period. Then, in the 1910s and 1920s, the need to emphasize the unity of the peoples of the Republic of China (in Chinese, Zhonghua Minguo, literally 'Country of the Zhonghua Minzu') as a single nation-state led to the increasingly popular argument that the Manchus, Mongols, Tibetans and Muslims were also part of the greater 中華民族. This position eventually became orthodox in the Republic of China, with five ethnic groups (zu 族) being recognized as making up the 中華 nation (minzu 民族).
The PRC further developed this multi-ethnic model by recognizing 56 民族 (translated as 'nationalities', but actually meaning 'ethnic groups') as making up a greater 中華 nation (again, minzu 民族). Many scholars have commented on the problems with using 民族 to translate both 'ethnic group' and 'nation', as well as the difficulty of developing a sense of multi-ethnic nationhood in the PRC, where ethnic nationalism tends to remain strong.