Rename versus Assignment

Rename changes the name or attributes of an existing relation, giving a new way to refer to it in subsequent queries.
   ρ_cus(customer)
   σ_{customer_city="Aurora"}(cus)

   ρ_{cus(cn, cs, cc)}(customer)
      makes the following query valid:
   σ_cc="Aurora"(cus)

Assignment creates a new relation.
   cus ← σ_{customer_street="Main"}(customer)
      also makes the following query valid
   σ_{customer_city="Aurora"}(cus)