Here in Puerto Rico, it was suggested to me that one had the flavor of "perhaps" and the other "maybe", but I always forget which is which.
if you are referring to "perhaps" being slightly more formal than "maybe", I don't think there is that difference between the Spanish "quizás" and "tal vez", at least in Peninsular Spanish. I see them both at the same level.
There is another "maybe" in Spanish which is "a lo mejor"; this phrase is a bit more colloquial than the others. Here are a couple of examples:
A lo mejor voy al parque hoy.
I may go to the park today./ Maybe I will go to the park today.
A lo mejor estás celosa.
You may be jealous./ Maybe you are jealous.
I don't think of the difference between "perhaps" and "maybe" being one of formality, though arguably "perhaps" is slightly elevated. I think of the difference as perhaps being a bit more theoretical or unlikely than a maybe. As I said, I don't recall which Spanish word aligned with which English word, so I'll have to ask again.
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