‘come together’ is used to say that different parts of a whole have been successfully combined. It may refer to a plan, a process, a project, a construction, etc. : ‘the project is starting to come together’
‘get together’ is an informal way of saying ‘meeting’ ; it can be used as a noun : ‘we’re having a get-together next Tuesday, would you like to come ?’ or a verb : ‘let’s all get together and try to sort this out’.