What is the difference between an Observed Holiday and an Observance?

An Observed Holiday is when a public holiday is celebrated which might not be the actual event's anniversary date.

For example, if July 4th (Independence Day) falls on a Saturday, it is "observed" on the Friday before as a holiday (and is usually a day off work). 

Observances, on the other hand, are remembrance, awareness and celebration-type days or events that are not normally days off work, like Valentine's Day, Mother's Day or Father's Day.