They represent different feelings.
glad is a more short-term happiness, like merry. You're likely to laugh when you're glad.
lycklig is a bigger feeling, more to do with fulfillment.

In some expressions, only one of them works.

In addition to what Arnauti said, something for speakers/learners of german:

"glad" and "lycklig" are "fröhlich" and "glücklich", I believe.

Notice that english "glad" is "froh" in german. Also, "färgglad"="farbenfroh".

It’s usually better translated with ’happy’, but it can correspond to English ’glad’ as well.