Relative vs Parallel Keys

Here is a tip on how you can remember the difference between a relative key vs a parallel key of a Major or minor keys.

Formulas:

Relative keys = same key signatures/different tonic. 
Parallel keys = same tonic/different key signatures

Relative key is a key that shares or has the same amount of sharps or flats (key signature) but has a different tonic than the key it shares.

For example, lets say we are working with c minor key. c minor has three flats in its key signature. So, what is c minor's relative key? c minor's relative key is Eb Major because Eb Major also has three flats in its key signature.

A parallel key shares the same tonic with another key , but has different key signatures. When working with parallel keys, one will be minor and one major key.

For example, c minor is parallel to C major because they have the same tonic. However, C major has no sharps or flats in its key signature. c minor has three flats.

You can also use the "Circle of Fifths" to help you understand relative and parallel keys better.