You are seeking words for classification of socio-economic status. This varies from culture to culture, and across time. Groups were previously more tightly stratified and with a clearer sense of hierarchy. A couple of possible candidates:
- The key concept is social class, often abbreviated to class. Wikipedia defines this as:
Social class (or simply "class"), as in a class society, is a set of concepts in the social sciences and political theory centered on models of social stratification in which people are grouped into a set of hierarchical social categories, the most common being the upper, middle, and lower classes.
Note also the terms "social category" or "social strata" which might also suit your purposes. A typical usage comes in their article on peasants:
A peasant is a member of a traditional class of farmers, either laborers or owners of small farms, especially in the Middle Ages under feudalism, or more generally, in any pre-industrial society. In Europe, peasants were divided into three classes according to their personal status: slave, serf, and freeman.
So not only did the "peasantry" form a class in their own right, they can also be subdivided into more specific classes.
- Socio-economic classification breaks down into smaller categories than traditional classes. For example the most current official socio-economic classification used in the UK is NS-SEC (which replaced two previous schemes, Socio-economic Groups and Social Class based on Occupation). A condensed three-category hierarchy is "1) Higher occupations, 2) Intermediate occupations, 3) Lower occupations". The current full scheme is:
1) Higher managerial and professional occupations 2) Lower managerial and professional occupations
3) Intermediate occupations (clerical, sales, service)
4) Small employers and own account workers
5) Lower supervisory and technical occupations
6) Semi-routine occupations
7) Routine occupations
8) Never worked and long-term unemployed
- Somewhat similar in concept to the above is social grade. In Britain social grading has traditionally been used to break down demographics of newspaper and magazine readership in order to provide extra information for advertisers. The following scheme of "social grades" is often used:
- A (upper middle class) Higher managerial, administrative or professional
- B (middle class) Intermediate managerial, administrative or professional
- C1 (lower middle class) Supervisory or clerical and junior managerial, administrative or professional
- C2 (skilled working class) Skilled manual workers
- D (working class) Semi-skilled and unskilled manual workers
- E (non working) Casual or lowest grade workers, pensioners, and others who depend on the welfare state for their income
Social grades from A to C1 are often combined as "ABC1" (middle or professional class), and from C2 to E combined as "C2DE" (lower or working class). So we often see people categorised in sentences like "The advertising campaign targets ABC1s" (Cambridge dictionary). This type of stratification is "social grading", and in some ways "C2DE" might be regarded as modern equivalents of the Medieval "peasantry".
One more modern tool used in identifying demographic types is segmentation. This identifies finer groups than "class" analysis, based on a more multidimensional analysis: age, income, assets and career: for instance "Mondeo man", "white van man", "motorway man" or "pebbledash people". So "social segment" may be much narrower than broad terms like "serf" in the original question, but is could well still be relevant to you, particularly in a modern context where social hierarchy is far less established in an age of less deference. A particularly good exploration of the concept is provided by the BBC, they are particularly used in political polling and marketing where older systems of social grading or classification have been found outdated or insufficiently targeted.
Not quite right for your example, but consider also caste. This is specific to certain cultures and a key feature is endogamy (marriage being restricted between castes, particularly between high and low castes). Reference.com, based on the Random House dictionary, defines it as:
(a) an endogamous and hereditary social group limited to persons of the same rank, occupation, economic position, etc., and having mores distinguishing it from other such groups; (b) any rigid system of social distinctions.
The sense (b) is often used metaphorically in other cultures, even if the insistence on endogamy is not present.
The four occupations or "four categories of the people" was a hierarchic social class structure developed in ancient China by either Confucian or Legalist scholars as far back as the late Zhou Dynasty and is considered a central part of the Fengjian social structure (c. 1046–256 BC). In descending order, these were the shi (gentry scholars), the nong (peasant farmers), the gong (artisans and craftsmen), and the shang (merchants and traders). These broad categories were more an idealization than a practical reality. This was due to commercialization of Chinese society in the Song and Ming periods, blurring the lines between these four hierarchic social distinctions. The system also did not figure in all other social groups present in premodern Chinese society. The definition of the identity of the shi class changed over time as well, from an ancient warrior caste, to an aristocratic scholarly elite, and finally to a bureaucratic scholarly elite with less emphasis on archaic noble lineage. There was also a gradual fusion of the wealthy merchant and landholding gentry classes, culminating in the late Ming Dynasty. — "Four occupations" on Wikipedia