William Blake and Richard Sheridan both wrote in the 18th century but their writings were very different. Why is this?
In a sense, the answer has to do with making explicit an unstated assumption in the question. That assumption is that all people alive at the same time write and think alike. That assumption is simply not true. Just as in the twenty-first century you would not expect hip-hop lyrics, New Formalist poetry, experimental language poetry, or comic books to be written in a similar style, you cannot expect every writer of the eighteenth century to have similar ideas and use identical literary forms.
The first difference between the two is that Richard Sheridan was an Irish playwright from a family with a strong theatrical tradition. His father, Thomas Sheridan, had been an actor who later became a teacher of elocution and writer about the topic. Richard Sheridan's plays were written for performance in the London theater and were intended to be commercial successes. Although he does satirize some of the excesses of the aristocracy, his work was intended to entertain large crowds through lively displays of verbal and situational humor. His work was quite successful popular entertainment following established comic genres.
Blake was not a playwright but a poet and was not attempting to write popular entertainment. He also lacked the literary education Sheridan absorbed in school and from his family. Instead, Blake's father was a hosier and Blake served as an engraver's apprentice. His advanced formal studies were not in literature or languages but in art at the Royal Academy. Blake's own work tended to be idiosyncratic, grounded in a religion he invented based on his visions and hallucinations (many contemporaries considered him insane). While he did find patrons to subsidize some of his work, he did not, in his lifetime, obtain a wide popular audience. His literary style was visionary and individualistic; even though he is often taught as part of the romantic "movement," in some ways he is closer to other eccentrics such as Christopher Smart than to educated aristocrats such as Shelley or Byron. While he influenced some of the romantics, his own poetic and artistic practice was grounded in his visionary ideals.
This question underlines two important axioms of literary history. First, a century is an artificial division (what if you said “The Titanic and the Ford Mustang were both in the 20th century”), and, second, “Literature reflects sociological and historical changes more often than it affects them”. In this case, Sheridan, a dramatist (and drama is the most reflective of literary genres), is following a change in class status that was the trademark of the “Age of Reason”, a time when Renaissance notions of royalty and privilege were giving way to enterprise, commerce, and accomplishment, a change that Sheridan both applauds and parodies in his plays, which the broader-class audience (broader than Restoration audiences) appreciated. Blake, on the other hand, at the close of the 18th and beginning of the 19th century, was at the forefront of Romanticism, a return to Nature, a re-examination of Man’s relation to the world, best expressed in the poetic genre, a personal voice and perspective. So, the different genres, the different ends of the (artificial) period, and the different views of society account for the admittedly wide gap between Sheridan and Blake. There is also a very real fin-de-siecle effect; as one century closes and another one opens, society anticipates sea-changes that are often self-fulfilling prophecies.