For Karl Marx, the stratification of social classes was the most significant source of societal conflict. Max Weber's definition of social class differs most notably from Marx's conception of the term in the sense that for Weber, social class and political class cannot simply be lumped together as a single entity.
Weber viewed and defined social and political realms separately in an attempt to put emphasis on the unique dynamic that power possesses in its own right, apart from economic interests. Moreover, he wanted to highlight the irrational features of power by making it clear that the rational interests of a class are not sufficient to explain the dynamics of society, particularly when comparing one society to another.
Weber's conception of what he calls "life chances" is a critical component of his understanding of social class. In Weber's view, an individual's class position is a direct determinant of how his life will turn out. The chances of a better life are, of course, higher for those in a higher social class and vice versa. The conception is evidence of Weber's view of the relationship between materialism and idealism. Social action, he believed, can be evoked by either or both as its driving force.
Marx is far more focused on the economic aspects of social stratification; most particularly, divisions of labor. In "Alienation and Social Classes" he wrote "Human alienation, and above all the relation of man to himself, is first realized and expressed in the relationship between each man and other men. Thus in the relationship of alienated labour every man regards other men according to the standards and relationships in which he finds himself placed as a worker" (Marx: 134).
Weber, while in agreement with Marx about the oppressive nature of social stratification, also believed that material possessions and a person's overall standard of living constitute the primary cause of class conflict. So whereas for Marx, the notion of alienation and oppression were seen as the chief aspects of social unrest, for Weber this unrest existed as a result of the power obtained from property ownership and other material possessions. Simply put, it was the 'haves' as opposed to the 'have nots' that had the most promising "life chances". The 'have nots' were therefore destined to stay poor while the 'haves' were destined to become more wealthy and more powerful.
Marx of course agreed with this perspective as well, however unlike Weber, he was unable to separate social class from economic class. So for Marx, feelings of alienation were just as influential on a person's social classification as were material possessions. For Weber, these entities did not necessarily have to co-exist; one could exist without the other. This is the primary point of divergence between Marx and Weber's conceptions of social class and social stratification.