How do subqueries work, exactly?

How do subqueries work, exactly?

I have a query that looks like this:
SELECT 'FY2000' AS FY, COUNT(DISTINCT SGBSTDN_PIDM) AS CHEM_MAJORS
FROM SATURN.SGBSTDN, SATURN.SFRSTCR
WHERE SGBSTDN_PIDM = SFRSTCR_PIDM
AND SGBSTDN_TERM_CODE_EFF = (SELECT MAX(SGBSTDN_TERM_CODE_EFF)
FROM SATURN.SGBSTDN
WHERE SGBSTDN_TERM_CODE_EFF <= '200002'
AND SGBSTDN_PIDM = SFRSTCR_PIDM)
AND SGBSTDN_MAJR_CODE_1 = 'CHEM'
AND SFRSTCR_TERM_CODE BETWEEN '199905' AND '200002'
AND (SFRSTCR_RSTS_CODE LIKE 'R%' OR SFRSTCR_RSTS_CODE LIKE 'W%')
AND SFRSTCR_CREDIT_HR >= 1
It returns a count of 48, which I believe is correct. However, I don't
understand why the subquery doesn't need SATURN.SFRSTCR in the FROM clause
in order to reference SFRSTCR_PIDM. I thought subqueries were self
contained and couldn't see the rest of the query?
But, if I add SATURN.SFRSTCR to the subquery, the count changes to 22. If
I take the AND SGBSTDN_PIDM = SFRSTCR_PIDM out of the subquery, the count
also changes to 22. Can someone explain this to me?