Pope and Swift do both use satire in the two works you mention, but they use different kinds of satire.
Pope in the mock-heroic, The Rape of the Lock, uses Horatian satire. He's making fun of upper-class customs, but mildly. He's having a joke at society's expense, but it's more teasing than condemning. He presents a woman putting on makeup as if she is a warrior preparing for battle. He's poking fun.
Swift in Gulliver's Travels, uses Juvenalian satire. Swift condemns his targets. His satire is not teasing or endearing, it is vehement and bitter. His targets are not exposed as silly, as Pope's are. Swift's targets are exposed as stupid, ridiculous, mindless, blood-thirsty, etc.
Again, both writers use satire, but the type of satire used by each is vastly different from that used by the other.
Alexander Pope's satire in "The Rape of the Lock" differs from Jonathan Swift's satire in Gulliver's Travels mainly in the scope of its ferocity. While Pope teases the upper class, chiding them for their foibles, Swift clearly hates the political structure he satirizes.
In "The Rape of the Lock," Pope satirizes the upper class of England with the quintessential mock-epic, which treats silly events with the seriousness of epics like The Odyssey or The Iliad. In this instance, Pope pokes fun at the upper classes, displaying the utter uselessness of their habits by treating them with excessive seriousness. However, he is doing so with a tongue-in-cheek attitude, and you'd be hard-pressed to find any truly nasty sentiments in the poem.
Swift's prose, however, positively drips with hatred. He doesn't merely poke fun at the upper classes; he compares all of humanity to savage, witless apes, and he suggests that common beasts (talking horses, to be more specific) are more intelligent than the human race. Indeed, at the end of the novel, Swift's Gulliver decides to complete remove himself from human society, citing it as coarse, vulgar, and useless. It's here that the real difference between Swift and Pope's satires lies. While Pope reveals the absurdity of humanity, he certainly doesn't utterly reject society; Swift, on the other hand, suggests that it would be better to live among beasts than humans.
Pope and Swift, contemporaries of one another in the eighteenth century, both used their famous works to satirize the society they lived in. However, the two writers used different styles of satire to address their appointed audiences.
Pope uses Horatian satire, which is a form of mild satire that teases the follies of individuals as part of the whole of society. Pope executes this through the mock-heroic form of The Rape of the Lock, his poem based on true events amongst his friends. Mock-heroic poems ridicule the heroic style and characters of classical epics. In the poem, we see members of high society engaging in a battle of cards, surrounded by many spirits, called sylphs, who encourage the intense emotions of the heroine, Belinda, and her antagonist, the Baron. Pope dramatizes the Baron’s petty prank of cutting off Belinda’s hair lock, escalating the feud to a battle of sylphs and catty insults. By poking fun at the individuals at this party, Pope is making a light-hearted commentary on the social customs of society as a whole. The audience finds themselves laughing both at the characters and themselves.
Jonathan Swift, on the other hand, is using the more caustic Juvenalian satire in his novel Gulliver’s Travels. Juvenalian satire is used to vehemently criticize an individual or institution. Unlike Pope’s light-hearted commentary on social customs, Swift is criticizing the England’s political structure and national attitude. Gulliver’s Travels is a parody of travellers' tales, a popular subgenre of the day. As Gulliver travels to various remote locations, Swift explores the many vices of the institutions around him, from political parties to societal entitlement. By attacking society as a whole, Swift aims to anger his readers and spur action for change.
Both writers encourage change in society by looking at the flaws of their contemporaries; however Pope mildly teases the individual to speak to the whole while Swift bitterly criticizes the whole to speak to the individual.