"Happy" covers everything from quiet satisfaction to a chemical high, and the words underneath it are not interchangeable. Some are calm, some are triumphant, some glow, some bubble over. Here is the happiness cluster from 1983, from settled to ecstatic.
In a state of peaceful satisfaction; happy with what one has.
settled, low-key
Happy and satisfied about a particular thing.
mild, specific
Happy and visibly showing it in manner or behavior.
bright, outward
Lighthearted and carefree.
carefree, sometimes heedless
Optimistic and confidently hopeful by disposition.
forward-looking temperament
Exuberantly joyful, sometimes with a mischievous edge.
childlike delight
Feeling or showing great happiness; full of joy.
wholehearted
Glowing with joy; happiness that shows on the face.
glowing from within
Lifted to high spirits, usually by a specific cause.
a peak, event-driven
Cheerful and bubbling over with energy and enthusiasm.
bubbling outward
Filled with great joy or triumph.
inner blaze of triumph
Openly expressing great happiness and triumph.
outward celebration
Feeling or expressing ecstatic joy or delight.
ecstatic
Serenely, blissfully happy.
a saintly calm
Feeling intense, almost chemical excitement and happiness.
a high
Content is the calm floor: quiet satisfaction with what you already have, no excitement required. Elated is a peak: lifted to high spirits by something specific, and temporary. "Happy" is the broad middle that does not commit to either. If you mean the settled kind, "content" is sharper; if you mean the soaring kind, "elated."
All high on the scale, different in shape. Elated is lifted up on the inside by an event. Ebullient is energy bubbling outward in your manner, more a temperament than a moment. Euphoric is the most extreme: an intense, almost chemical high.
Both are the joy of triumph. Exultant is the inner blaze of having won. Jubilant is that triumph expressed outward, the cheering and celebrating. One is felt, the other is shown.
Elated means lifted to high spirits, usually by a specific cause like good news. Euphoric is more extreme: a state of intense, almost chemical excitement. On the 1983 scale elated sits at 7 and euphoric at 9.
Content is the best fit: a peaceful satisfaction with what you have. Pleased is similar but tied to a particular thing. Both are gentle and low-key, the opposite of an excited peak.
Euphoric sits at the top, an intense almost chemical high. Beatific and rapturous are nearly as strong but calmer: beatific is serene bliss, rapturous is ecstatic delight.
Blithe means lighthearted and carefree, but it can carry a critical edge of being heedless or unconcerned, as in "blithe disregard." It is not always a compliment.
1983 maps the happiness cluster, and hundreds of others, as a field you can tap through, with recorded audio for every word and quizzes that test whether you can place a word among its neighbors.