"Earlier is better" is what we would say when given a choice of two times. "The sooner the better" is what we would say when there is a sense of urgency to the situation. Does that help?

Treat this like a gradient (or number line) from "earliest" to "latest". "Earlier is better" implies multiple points on the gradient (exact times). Whereas "The sooner the better" asks the person to get as close to the "earliest" side of the gradient as possible. "The sooner the better" is synonymous with "as quickly as possible." Whereas "earlier is better" is synonymous with "I prefer the earliest time." Examples: "We can go to the store at 6am or 8am." "Earlier is better." "How quickly should I finish my dinner?" "The sooner the better."

Merhaba Pelin. I agree with Julie. The second one is another way of saying 'as soon as possible' - i.e. there's a sense of urgency. The first one could occur in a context like this one: Paul: 'Shall I come to the party at 10pm?' Sarah: 'If you could come a bit earlier, that would be better.'