The distribution code for normal distributions would be shown in Box 7 on your 1099-R. This would normally apply to both Federal and State returns. I know of no instance where a state would have a different distribution code than what is shown for your Federal distribution code. A normal distribution from a 401K would have a distribution code of "7".
ESOP is an acronym for "Employee Stock Option (or Ownership) Plan". Normally any purchase made under these types of plans would appear as a line item on your Form W-2. If you converted your ESOP shares and sold them you would or should have, received a Form 1099-B showing the sale of shares.
I have enclosed links that further explain the items that you are questioning. The distribution codes for Form 1099-R are linked on Page 13 of the 1099-R instructions.
Instructions for Form 1099-R
How do I enter ESPP sales
What is an ESOP?
@paulstek
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