Different kinds of happiness cause different effects and penetrate at different levels. They mingle with other emotions, too, as I'm sure you might have noticed, which makes it hard to distinguish between say: bittersweet and melancholy.
Bittersweet is just as it sounds. It's appreciation for something, tinged with regret. Or gratitude mixed with disappointment. Joy with loneliness. It's saying goodbye to something that you're not sure you want to see go. Like watching your childhood and realising that that part is over or was never there to begin with.
Melancholy is slightly different. It encorporates the same mixture of "happy" and "sad", but it's more like a sadness that feels good. Like a mixture of pain and pleasure...which it is, in a way. Sometimes it feels like the cold pain-pleasure you get if you orgasm too many times in a short time period, or press on a nerve too hard and it starts to tingle. It's rainy days. It's the odd cool stillness where there's a quiet "drip, drip, drip" of an imaginary faucet inside your head. Sometimes you want it to go away so you can stop feeling so heavy inside, but there's something about the sheer depth of this feeling that makes you want it to stay a while...it's not often a feeling penetrates right down to your core. (Can you tell I have a little more experience with melancholy than bittersweetness?)
On the other end of spectrum, there's overwhelming joy and revelation.
Both are heady emotions, and quite similar.
Overwhelming joy is happiness to the point of tears. It's relief. Sometimes it's living vicariously through someone else. It feels like a carbonated drink that's been shaken up. It bubbles and froths and spills over onto other people. It's disbelief mixed with exictement. It's the moment where the world ceases to be real and becomes precisely what you hoped it would be, at least for a moment.
Revelation draws on the same uplifting qualities of joy, but instead of bubbling and frothing, it swells like a wave and crashes inside of you instead of spilling over. The world becomes sharper, clearer, more real as opposed to less real. There's the distinct impression of walking through and around reality as if you are inside and outside of it at the same time. Like Neo when he realised he was both inside and outside of the Matrix. It is relief also, as a problem has suddenly been "completely" solved.