How do SQL EXISTS statements work?

Question

I\'m trying to learn SQL and am having a hard time understanding EXISTS statements. I came across this quote about \"exists\" and don\'t understand something:

Answer 1

You can produce identical results using either JOIN, EXISTS, IN, or INTERSECT:

SELECT s.supplier_id
FROM suppliers s
INNER JOIN (SELECT DISTINCT o.supplier_id FROM orders o) o
    ON o.supplier_id = s.supplier_id

SELECT s.supplier_id
FROM suppliers s
WHERE EXISTS (SELECT * FROM orders o WHERE o.supplier_id = s.supplier_id)

SELECT s.supplier_id 
FROM suppliers s 
WHERE s.supplier_id IN (SELECT o.supplier_id FROM orders o)

SELECT s.supplier_id
FROM suppliers s
INTERSECT
SELECT o.supplier_id
FROM orders o