Why the recording does not match your guitar
A song recorded with the guitars tuned a half step down sounds one semitone lower than the same chords played in standard tuning. Play along in standard tuning and every chord clashes by a semitone, even though your fingers are on the right frets.
The fix: raise the recording
Raise the recording by 1 semitone: press + beside Key once. The recording is now at standard-tuning pitch, and the chord shapes in the lesson or the tab fit your guitar again. For a recording tuned a whole step down, which players call D standard, press + twice.
The other direction
You can fix it from your side instead: tune your guitar down a half step and leave the recording alone. That is fine for one song. If you are playing several songs in different tunings, or moving between a guitar and a keyboard, raising the recording saves retuning every time.
How to tell how a recording is tuned
Play the first chord of the song along with it. If your chord rings a semitone higher than the recording’s, the song is probably tuned down half a step: press + once and play it again. If it still clashes, try +2.
Raise it, do not lower it
The direction trips people up. The recording is the thing that is too low, so it is the recording that goes up. Pressing − would move it further from your guitar, to two semitones away.
Whole step down, and lower
Some bands tune down further than a half step. A whole step down means pressing + twice, and a step and a half down needs +3. When you are not sure how far down a recording is, add one semitone at a time until your chord shapes sit inside the song without clashing.