Employer's state ID number is not listed in box 15, but Employer ID number (EIN) is in box b. Is that the same number?

No, the Employer State ID number (box 15) is issued by the department of revenue or similar agency in the state where the business is located . EIN (box b) is issued by the IRS.

You can use the federal ID number that is listed in box "b" if there is no state ID number listed on your W2 in box "15".