Capitalism and Feudalism are both examples of class societies, but are not the same. Both have had working and owning classes, but the nature of relation to production is different, thus the class mechanisms at play are different. Engels sums it up succinctly in questions 7-10 of Principles of Communism, but I’ll only copy 7 and 8, as they are more relevant here:

Question 7 : In what way does the proletarian differ from the slave?

Answer : The slave is sold once and for all; the proletarian must sell himself daily and hourly. The individual slave, the property of a single master, is already assured an existence, however wretched it may be, because of the master’s interest. The individual proletarian, the property, as it were, of the whole bourgeois class, which buys his labour only when someone has need of it, has no secure existence. This existence is assured only to the proletarian class as a whole. The slave is outside competition, the proletarian is in it and experiences all its vagaries. The slave counts as a thing, not as a member of civil society; the proletarian is recognized as a person, as a member of civil society. Thus, the slave can have a better existence than the proletarian, but the proletarian belongs to a higher stage of social development and himself stands on a higher level than the slave. The slave frees himself when, of all the relations of private property, he abolishes only the relation of slavery and thereby becomes a proletarian himself; the proletarian can free himself only by abolishing private property in general.

Question 8 : In what way does the proletarian differ from the serf?

Answer : The serf enjoys the possession and use of an instrument of production, a piece of land, in exchange for which he hands over a part of his product or performs labour. The proletarian works with the instruments of production of another for the account of this other, in exchange for a part of the product. The serf gives up, the proletarian receives. The serf has an assured existence, the proletarian has not. The serf is outside competition, the proletarian is in it. The serf frees himself either by running away to the town and there becoming a handicraftsman or by giving his landlord money instead of labour and products, thereby becoming a free tenant; or by driving his feudal lord away and himself becoming a proprietor, in short, by entering in one way or another into the owning class and into competition. The proletarian frees himself by abolishing competition, private property and all class differences.