分手 means "separates with someone" or "break up with someone". 告别 means "say good bye to someone“. Examples: 1. 我和女朋友分手了。 2. 我们在机场分手，他去纽约，我去芝加哥。 3. Tom即将去英国留学，他向朋友和家人一一告别。 4. 他明天就去美国工作了，他的朋友们今晚为他举办了一场告别晚会。

分手often used with your girlfriends ,it means your lover realationship broked up.告别 equal to say goodbye with your friends .

分手 是 生離 而 告別 可能是 死別 (告別式/生前告別式)

Sorry for that these two phrases are not always verb in Chinese. 分手 means breaking up, usually is for relationship only. You may say I would like to make this relationship with a beautiful 分手 with a lover to thank for her sharing time with you. 告别 means farewell, also means to take a leave if you don't want to go back is fine because the decision is made by you.

“分手” means breakup, and “告别” just means say goodbye. But sometimes in written chinese,“分手”can also express say goodbye.