Is there any different for foreign key to be serial instead of integer

I came across a lot of similar example for foreign key

CREATE TABLE orderinfo
(
orderinfo_id serial ,
customer_id integer NOT NULL,
date_placed date NOT NULL,
date_shipped date ,
shipping numeric(7,2) ,
CONSTRAINT orderinfo_pk PRIMARY KEY(orderinfo_id),
CONSTRAINT orderinfo_customer_id_fk FOREIGN KEY(customer_id) REFERENCES
customer(customer_id)
);

instead of let customer_id being type as integer, can i let it be serial? is there any difference?

if the table referenced by customer_id is having primary key typed big serial, customer_id shall be declared as bigint
?

Thanks