The OED, updated 2008, has 8 entries each of which has about 3 subsections. Race, in this 'group' meaning, is a word that has many connotations and is somewhat imprecise, and even context does not always help as can be seen from the accompanying notes.
Race and species differ. Species is the greater. A safe definition to distinguish race from species is:
OED
Race 5.a. A breed or stock of animals or plants; (Biology) an interbreeding population within a species that is genetically and morphologically distinct from the members of other such populations of the same species, esp. through cultivation or breeding or as a result of geographical or ecological isolation.Sometimes equivalent to subspecies; sometimes (esp. in Botany) used to denote a rank between subspecies and variety.
1973 BioScience 23 523/1 We are dealing with a single species of honeybee, Apis mellifera, the races of which differ very little in appearance or structure.
The difficulty arises when the subject is human and politics and sensitivities come into play...
**Race I. A group of people, animals, or plants, connected by common descent or origin.In its widest sense the term includes all descendants from an original stock, but may also be limited to a single line of descent or to the group as it exists at a particular period.
1.a. A group of people belonging to the same family and descended from a common ancestor; a house, family, kindred.
2000 E. S. Belfiore Murder among Friends i. 16 The Argive women supplicate Theseus on the basis of kinship, since they, like him, belong to the race of Pelasgos.
b. An ethnic group, regarded as showing a common origin and descent; a tribe, nation, or people, regarded as of common stock. In early use frequently with modifying adjective, as British race, Roman race, etc. Frequently overlapping with, and difficult to distinguish from, sense 1c and in some cases also sense 1d.
2005 D. McWilliams Pope's Children xxiv. 271 Back in mainland Europe, it feels like the Jews and the Paddies are the only two entrepreneurial races in Europe.
c. A group of several tribes or peoples, regarded as forming a distinct ethnic set.Esp. used in 19th-cent. anthropological classification, sometimes in conjunction with linguistic groupings. Frequently overlapping with, and difficult to distinguish from, both sense 1b and sense 1d.
2004 R. Weitz Rapunzel's Daughters i. 20 In his influential 1916 book, The Passing of the Great Race , Madison Grant argued that ‘the citadel of civilization will fall’ if the Nordic race..wiped itself out through intermarriage with the ‘brunet’ races of southern and eastern Europe.
d. According to various more or less formal attempted systems of classification: any of the (putative) major groupings of mankind, usually defined in terms of distinct physical features or shared ethnicity, and sometimes (more controversially) considered to encompass common biological or genetic characteristics.
In early use usually applied to groups of people with obviously distinct physical characteristics such as skin colour, etc. An influential early system was that of J. F. Blumenbach De Generis Humani Varietati Nativa (1775), which, on the basis of skin colour and conformation of the head, divided the human species into five races, the American, Caucasian, Ethiopian, Malay, and Mongolian, and assigned them qualitative ranking. A similar division into six was proposed by Goldsmith (cf. quot. 1774). In particular contexts (e.g. former European colonies or areas of the United States) adherents of a theory of race have frequently applied only a simple two-term distinction (such as ‘black’ and ‘white’).
Now often used more generally to denote groups of different cultural or ethnic origin (esp. as forming part of a larger national community), in which context it frequently overlaps with, and can be difficult to distinguish from, senses 1b and 1c; examples have been placed at this sense where distinct physical features play an important role in how race is conceptualized. In recent years, the associations of race with the ideologies and theories that grew out of the work of 19th-cent. anthropologists and physiologists have led to the word often being avoided with reference to specific ethnic groups. Although it is still used in general contexts, it is now often replaced by terms such as people(s), community, etc.
1997 Sciences Mar. 22/1 True races may not exist, but racism does.
2005 P. S. Parker Race, Gender, & Leadership i. 1 A White middle class feminine ideal that paradoxically excludes the leadership experiences of women of different races and class statuses.