What is the difference between "CONTACT" contact_id and "INVOICE" customer_id

What is the difference between "CONTACT" contact_id and "INVOICE" customer_id

When I'm creating the Invoice it is asking the "customer_id" and I created the contact person, get the "contact_id".
I try to pass this contact_id to create invoice but it is throwing the error 

{
    "code"57,
    "message""You are not authorized to perform this operation"
}

And I given the valid organization_id , Content-Type, Authorization  but still I'm getting the same error