Come and go: differences

 Come and go 

Come is used for movements to the place where the speaker or hearer is. 

• Come to me. (Movement towards the speaker) 

• 'Alice, can you come here?' 'Yes, I am coming.' (NOT I am going.)

 • Can I come and sit beside you? (Movement towards the hearer) 

Go is used for movements to other places.

 • Let's go and see them. (NOT Let's come and see them.) 

• I want to go and live in the hills. (NOT I want to come and live in the hills.)