i.e. "It's your fault",
"You are the one to blame."
Fault is a geological term we use to point out the error, crack, deficient area of skill -- "It's your fault" This is your mistake, your hole in the ground -- thus there is a specific error. You can point at it.
Blame is to accuse, or denounce but not with the specific reason as a requirement. Blame is a short word for Blaspheme as well.
They are synonymous certainly, but I don't feel they are the "same" in meaning.
Etymology
blame (v.) c. 1200, "find fault with;" c. 1300, "lay blame on," from Old French blasmer (12c., Modern French blâmer) "to rebuke, reprimand, condemn, criticize," from Vulgar Latin*blastemare, from Late Latin blasphemare "revile, reproach" (see blaspheme). Replaced Old English witan with long "i." Related: Blamed; blaming.
damn (v.) late 13c., "to condemn," from Old French damner "damn, condemn; convict, blame; injure," derivative of Latin damnare "to adjudge guilty; to doom; to condemn, blame, reject," from noun damnum "damage, hurt, harm; loss, injury; a fine, penalty," possibly from an ancient religious term from PIE *dap- "to apportion in exchange" [see Watkins]. The Latin word evolved a legal meaning of "pronounce judgment upon." Theological sense is first recorded early 14c.; the optative expletive use likely is as old.
Fault
fault (v.)
"find fault with," mid-15c. from fault (n.). Earlier it was used in an intransitive sense of "be deficient" (late 14c., Scottish). Related: Faulted; faulter; faulting.
fault (n.)
late 13c., faute, "deficiency," from Old French faute, earlier falte, "opening, gap; failure, flaw, blemish; lack, deficiency" (12c.), from Vulgar Latin *fallita "a shortcoming, falling," from Latin falsus "deceptive, feigned, spurious," past participle of fallere "deceive, disappoint" (see fail (v.)).
From what I get from this, you can Amend a Fault, by learning better skills, education, and experience. The fault may also be singular and everything else you did was just fine.
What you are Blamed for is not a mistake but blackness a vileness of your soul - thus you need forgiveness, or Grace
That you rigged the sail improperly during the storm would be Your Fault
That you are a Jonah, you are Blamed for the storm
