There's also the point that if you play a barre chord with your pinky three frets up on the high E string, the chord is unresolved and can serve as either major or minor. The classic Dm and Em are obtained by squishing your fingers across from the F chord you already have - use the 2nd finger (nearest the bass) to stop the low three strings, the next (third finger) stops two strings, the index finger does the E string - 222221 = Dm, move it up two frets for Em. You'll find in practice that people pick around these shapes, leaving strings open, and rarely playing the full closed chords.