Use 'melancholic' when someone is sad without an obvious reason, not just for any sadness. Even with all her achievements, she felt a melancholic sense during her quiet evenings.
Pro Tip 2/2
Temporary Mood
'Melancholic' often suggests a temporary state of sadness, not a long-term condition. The cloudy skies and drizzle left him in a melancholic mood, unlike his usual cheerfulness.