They have about the same meaning of telling someone to leave. Both phrases are rude things to say to someone, but I feel "Get lost." is more offensive. The phrases can be used descriptively too, in which case they have different meanings which are not rude. - He went away. = He left for some other place. - He got lost. = Going somewhere, he got confused about his bearings (directions).

"Go away" means to leave a place. Ex: He went away that day and I haven't seen him so far. If you are tired and you don't want to talk or listen to someone then you can say "Go away!" It is rude but not as rude as "Get lost" "Get lost" means to lose direction. Ex: Excuse me, can you tell me please, what place is this? I am lost! I must go to the train station. If you say it to someone, then you don't want to see that person anymore. "You broke my heart! Get lost!" (I really don't want to be in this situation). "Get lost" is used when someone cannot find their way.

I believe that is a Formal and informal

Thank you dear Michael.

As an instruction, "get lost" is aggressive and rude, normally deliberately so. It's much stronger than "go away", and people often move to "get lost" if "go away" doesn't work with someone who is bothering them.