You can glean the answer to this question from the answers to Questions 7 through 12 in “Draft of a Communist Confession of Faith.” There, Engels tells us that the proletariat in an industrial society differs from other underclasses because of the particular way in which it is exploited and the nature of the option it has for overthrowing its exploitation and becoming free.
In Question 9, Engels says that the proletariat comes about because of the introduction of machinery and factories. Before these things came about, workers could make entire products using a few tools that they could own. When machinery and factories arose, only capitalists could afford to own the means of production and workers’ jobs became narrower and narrower. Instead of making a product, they performed one little part of making a product. This is the nature of the proletariat.
In Questions 10 through 12, Engels lays out the differences between proletarians on the one hand and slaves and serfs on the other. As I mentioned before, he says that the different underclasses are exploited in different ways. Slaves are property and are owned by individuals. Proletarians are not legally property, but are still owned, in essence, by the entire bourgeois class because that is the class that will buy the proletarians work if it wants to. Slaves have less status in society, but may have better material conditions because they are the responsibility of an individual who must care for them. Serfs are different from the proletarians because they have a right to use a given piece of land and because they can increase their income by working harder. Proletarians have neither of these things; they do not own their means of production and they must work for whatever pay is offered.
The proletariat also differs from slaves and serfs in terms of what they must do to become free. Slaves can become free by abolishing the idea that people can be property. A serf can become free by “driving out his feudal lord and becoming a property owner himself.” By contrast, the proletariat can only become free if it destroys the entire idea of property.
So, the main differences between the proletariat and these other underclasses are A) the nature of their exploitation and B) what they have to do to end the exploitation.