Does tuning affect key?

If I am playing a song in standard tuning that is in the key of Em, if I tune down to the key of Eb am I still in the key of Em? Say that I am playing chords C, Em and Am. If I tune down to Eb but still play the same finger positions, am I still in the key of Em? Thanks!

No you are no longer in the Key of Em. The Cmaj chord becomes a Bmaj...the Em becomes D#m and the Am becomes a G#m. So that could be in the Keys E, B or others.

I'm just going to clarify what Bodom stated, with some visuals.

If you are tuned for "Standard" your E string's Frets would be:

Frets: |0 |1 |2 |3 |4 |5 |

Notes: |E |F |Gb|G |Ab|A |

If you tune down the E string a half step, the Guitar's "E" string is now "Eb" and the Frets would read:

Frets: |0 |1 |2 |3 |4 |5 |

Notes: |Eb|E |F |Gb|G |Ab|

If you play the 5 fret on the 6th string tuned half a step down, what note is it? Is it the same as the fifth fret on the 6th string in standard tuning?

The same applies to a chord, because that is all a chord is; multiple notes. If the notes change, so does the chord.. It may look the same, but if you listen, you'll notice it doesn't sound the same. (same is true with those basic Barre chords, if you play the G Maj Barre chord on the thrid fret, it looks the same as though you played the same fingering on the fifth fret, except now it sounds like an A Maj chord)

Hope both our posts helped.