I learnt from Guitarists on this site if you add D#, it = blues scale - Six notes.

But I don't know If A,C,D,D#,E,G = A Blues scale or A minor blues Scale.

The "Blues Scale" has all the notes of the "Minor Pentatonic", plus the flatted fifth of the Natural . {A-C-D-Eb-E-G}.
This six-note scale has a minor tonality, becouse of the interval from the root to the third of the "Minor Natural" , wich is a "Minor Third"(1 1/2 steps).
(A-C)= 1 1/2 steps= Minor Third

The addition of the "Blue Note" forms a Chromatic tone(D-Eb-E) characteristic of the blues music.
I heard a musician say, that the blue note is a troubled note, that doesn`t know what to do in the middle of the other notes, and needs to be resolved; Jazz musicians, play more chromatic tones, and choose to leave those added notes unresolved.