"For instance, there are two different un- prefixes in English: one meaning 'not, opposite of', the other meaning 'reverse action, deprive of, release from'. The first prefix un- 'not' is attached to adjective and participle bases while the second prefix un- 'reverse action' is attached to either verb or noun bases." (From wikipedia)

Since we're talking about an adjective base here, "not happy" === "unhappy".