楽しい＝adjective 楽しみ＝noun or verb ex: パーティーは楽しいです。 　　パーティーが楽しみです。 The first example means that you think a party is fun. The next one is that you are planing to have(or go to) a party and you are looking forward to it. In this case, 楽しみ is a noun. It is the noun form of the verb 楽しむ (to have fun), meaning It's the result of verb conjugation. Now look at the another example. パーティーを楽しみました。 In this case, 楽しみ is a verb. Let me make it clear. 犬＝noun, 猫＝noun, 車＝noun. If it makes sense when you think about other nouns like above, and + "です", that means it is a noun. 楽しみです。　 犬です。　猫です。　車です。 If it doesn't make sense when you use other nouns + "ます", that means 楽しみ is a verb. 楽しみます。　犬ます。　猫ます。　車ます。

楽しみ means" looking forward to" 楽しい means "fun"