American Board of Medical Specialties
Board eligible/board certified
ABMS is the gold standard and often considered to be the only BE/BC that counts (by hospitals, medical centers, etc).
The DO school doesn't make that much difference. ACGME res dir rarely make much of a distinction between the schools...they tend to group them together.
Studies indicate that board scores are weighted low on the list of what ACGME res dir look for when ranking applicants. ~7 out of 10, if I remember correctly. When I was applying, I told them that I passed and never provided the #s and I did not sit for part 2 until after the interviews. It did not matter. AOA programs tend to be more concerned about board scores, though I did not apply to any. This is what my classmates relayed to me.
Get Isserson's book on 'Getting Into A Residency', it explains most of what you need to know.