Major and minor keys that share the same key signature are called relative keys. For instance, the C major key and the A minor key are relative keys because they share the same key signature.
From the tonic of a minor key, we can obtain the tonic of its relative major key by applying the ascending minor third. For instance, when we apply the ascending minor third to A, we obtain C. This tells us that the A minor key has the C major key as its relative major key.
We can use this fact to write any natural minor scale if we know only how to write major scales. For instance, if we want to write the C natural minor scale, we must apply the ascending minor third to C, which gives Eb. Then, we should find the note names of the Eb major scale and rewrite them in the form of the scale starting from C. The result is shown in the next figure.
Figure: The notes of the Eb major scale rewritten as the C natural minor scale
Similarly, from the tonic of a major key, we can obtain the tonic of its relative minor key by applying the ascending major sixth. For instance, when we apply the ascending major sixth to C, we obtain A. This tells us that the C major key has the A minor key as its relative minor key.
A major and minor key with the same tonic are called parallel keys. For instance, the D major key and the D minor key are parallel keys.
The tonality and key are not the same. The tonality is related to the tonic. A key and its parallel key are two different keys but they belong to the same tonality because they share the same tonic. For instance, the C major key and the C minor key are two different keys belonging to the same tonality.