semitones

There's two options here.  You can move the capo up 2 frets and play the exact same fingerings you would without the capo (just two frets higher). Or you can transpose it up two semitones and play new fingerings without a capo. Example: If you're playing a song that has the chords G C and D and you want to transpose it to A D and E (two semitones up),  you could just put a capo on the second fret and play G C and D normally, but now you'd be playing the G fingering on the 5th Fret, not the third.  Am I making sense?  If you wanted to skip the capo altogether, just play A D and E instead of G C and D.

True.  Also, if you put a capo and play the same chords you're changing the key.   But if you change the chords down same number of semitones as the capo you're back to playing in the same key.  This is how we sometimes make a difficult song easier to play.