A 7th chord is constructed by taking a standard triad and stacking an extra third on top. Both of the chords in this game are built on a Major Triad, but feature a different 7th note:
Major 7: Root + 4 semitones + 3 semitones + 4 semitones
Dominant 7: Root + 4 semitones + 3 semitones + 3 semitones
Listen for the emotional qualities of these chords. Major 7ths often sound dreamy, jazzy, or resolved. Dominant 7ths feature a flatter, "minor" 7th interval which makes them sound bluesy, tense, and unresolved (like they want to lead into another chord).