What is a diference between いく and あるく?


As I understand both means "walk". What is a difference here? I think that いく
is more like "move" somewhere and あるく means literally walk. Is that right or
something else?




YES, that make sense and you're right.  
As a Japanese native speaker I think if you have already been able to go
somewhere with someone then you say "あるく" due to you can walk and to go the
place on the other hand you just talking or messaging someone to go somewhere
then you say "いく".  
So I think the difference between them is just your situation when you say to
go somewhere.

