"Glad" and "happy" are almost interchangeable as synonyms
Somebody can feel happy for no reason, usually a more subdued enduring sense of well-being, satisfaction, and enjoyment.
But there has to be something concrete to feel glad about, usually associated with a short-term experience of pleasure, joy, or delight through some immediate cause.
You can say that "happy" is "happier" than just "glad".
In a business letter expressing pleasure, then you would use "glad", rather than "happy".