Perhaps and maybe are both adverbs used to express uncertainty or possibility, but there are subtle differences in their usage. Maybe is generally considered more informal and is often used in spoken English. Perhaps sounds a bit more formal and is often used in written English. Perhaps also suggests a slightly higher degree of possibility than maybe. Think of it this way: perhaps leans towards a more likely chance, while maybe is more open-ended.
Let's look at some example sentences:
Maybe I'll go to the party. (Informal. It's possible, but not certain, that I'll go.)
Translation: There is a possibility that I will go to the party, but I am not sure.
Perhaps I'll go to the party. (Slightly more formal. There's a somewhat better chance I'll go.) Translation: It is possible that I will go to the party; there is a higher chance than the previous sentence.
Maybe it will rain tomorrow. (Informal. There's a chance of rain.) Translation: There is a chance of rain tomorrow.
Perhaps it will rain tomorrow. (Slightly more formal. The chance of rain seems a bit higher.) Translation: There is a possibility of rain tomorrow; the possibility is a bit higher than the previous sentence.
Maybe she's right. (Informal, expressing uncertainty about her correctness.) Translation: It is possible that she is right.
Perhaps she's right. (Slightly more formal, a slightly stronger suggestion of the possibility that she is right.) Translation: There is a possibility that she is right; the possibility is a bit higher than the previous sentence.
While the difference might seem small, using the right word can make your English sound more natural and sophisticated. Pay attention to the context and choose the word that best fits the situation.
Happy learning!