Difference between Happily and Gayly

HAPPILY vs GAYLY: ADVERB

In a joyous manner
In a happy manner or state; in happy circumstances.
In an unexpectedly lucky way
By chance; perhaps.
By good chance; fortunately, successfully.
In a happy or cheerful manner; with happiness.
With good will; in all happiness; willingly.
With address or dexterity; gracefully; felicitously; in a manner to insure success; with success.

By good fortune; fortunately; luckily.
In a happy or pleasing way or state; in pleasant or fortunate circumstances; with happiness or joy.
With address, skill, dexterity, or aptness; dexterously; felicitously; aptly; gracefully.
By chance; peradventure; haply.
Synonyms Haply, Happily. Haply, now rarely used in prose, means by chance; happily, by a happy chance.
Prosperously, successfully, contentedly.

Comfortably, Pleasantly, Quietly, Gaily, Willingly, Enthusiastically, Gladly, Cheerfully, Joyfully, With happiness, Gayly, Mirthfully, Jubilantly, Blithely, Merrily

Indolently, Suavely, Saucily, Serenely, Prettily, Gaudily, Daintily, Jauntily, Gaily, With happiness, Jubilantly, Blithely, Merrily, Happily, Mirthfully

Delightfully, Seamlessly, Happier, Happy, Readily, Comfortably, Pleasantly, Quietly, Gaily, Willingly, Gladly, Gayly, Mirthfully, Blithely, Merrily

Sweetly, Languidly, Flamboyantly, Coquettishly, Regally, Indolently, Suavely, Saucily, Serenely, Gaudily, Daintily, Gaily, Blithely, Merrily, Mirthfully

We are both happily starting the maintenance program.
You can definitely barhop happily on that street.
Brazil heist finally living happily and in peace.
Gobble them down happily along with your coworkers.
Shayna grew up dreaming about happily every after.
Politely say no and live your life happily.
We will happily recommend you at any opportunity.
Williams and Dunst, happily, are the real stars.
He happily gave up everything for us and when we realized this we happily give up everything for him.
There are enough retailers out there that will happily accommodate their customers and I will happily patronize them!

But when I looked up wonderingly at this unusual demonstration, she only danced off gayly waving her hand at the door.
And, what was worse, he was so gayly and cynically conscious of having done me.
The story of her experiences is very gayly and very merrily set forth.
Charity, Going forth gayly in the morning to woo the world with smiles.
She had come out almost gayly, and now she was trembling.
She gayly sat down beside Alyosha on the sofa, looking at him with positive delight.
Gayly they ring, while people sing, songs of good cheer, Christmas is here.
An orchestra, riders on gayly colored bicycles led the celebrants.
Helen as the trio gayly hurried down stairs.
He mounted his horse and gayly cantered away.