Use of "glad" and "happy"

Going on with what Collane said, there are some moments when you wouldn't say "glad" over "happy" but these moments will hardly ever arise.

For example, happy can be used to describe something that has been stricken with good fortune. Like, "a happy birth" or "a happy season." Though that concept can be hard to grasp. Not to be confused with when someone says "happy go lucky" which means someone is cheerful to a fault, which is also not interchangeable with glad. It can also be used to describe someone who is apt to take action swiftly, like "trigger-happy" to describe someone who will pull the trigger way too fast or too much.

And finally, some may think that "happy" is less formal than "glad."

"Glad" and "happy" are almost interchangable as synonyms. The only case that I can think of where there's a real difference is that "glad" isn't used as a general state of mind; there almost always has to be a direct, immediate cause of being glad. That is, somebody can feel happy for no reason, but there has to be something concrete to feel glad about. Otherwise, they're nearly the same.

e.g.

"I'm happy for you."

"I'm glad for you."

"That makes me happy."

"That makes me glad."

"I feel happy today."

But

"I feel glad today" is just... awkward and weird-sounding to me. I think it's still technically correct, though.

"Glad" is experiential/'required valence'. 'to be glad' sounds very strange when used intransitively.

You shouldn't say "I'm glad" unless there's an omitted object.

For example:
"How are you?"
"I'm happy." NOT "I'm glad."

Similarly:"I support.""It interests."