The difference between Melancholy and Sad

When used as adjectives, melancholy means affected with great sadness or depression, whereas sad means feeling sorrow.

Melancholy is also noun with the meaning: black bile, formerly thought to be one of the four "cardinal humours" of animal bodies.

check bellow for the other definitions of Melancholy and Sad

Melancholy as an adjective (literary):

Affected with great sadness or depression.

Examples:

"'Melancholy people don't talk much."

Melancholy as a noun (historical):

Black bile, formerly thought to be one of the four "cardinal humours" of animal bodies.
Melancholy as a noun:

Great sadness or depression, especially of a thoughtful or introspective nature.

Sad as an adjective:

Emotionally negative. Feeling sorrow; sorrowful, mournful. Appearing sorrowful. Causing sorrow; lamentable. Poor in quality, bad; shameful, deplorable; later, regrettable, poor. Of colours: dark, deep; later, sombre, dull.

Examples:

"She gets sad when he's away."

"The puppy had a sad little face."

"It's a sad fact that most rapes go unreported."

"That's the saddest-looking pickup truck I've ever seen."
Sad as an adjective (obsolete):

Sated, having had one's fill; satisfied, weary.
Sad as an adjective (obsolete):

Steadfast, valiant.
Sad as an adjective (obsolete):

Dignified, serious, grave.
Sad as an adjective (obsolete):

Naughty; troublesome; wicked.
Sad as an adjective (slang):

Unfashionable; socially inadequate or undesirable.

Examples:

"I can't believe you use drugs; you're so sad!"
Sad as an adjective (dialect):

Soggy (to refer to pastries).
Sad as an adjective (obsolete):

Heavy; weighty; ponderous; close; hard.

Examples:

"sad bread"