The difference between 'credit' and 'accredit'?

Both verbs seem to mean the same thing -- to attribute 'X' to Mr. 'Y'. On looking it up, I found:

credit - publicly acknowledge a contributor's role in the production of (something published or broadcast).

accredit - give credit to (someone) for something.

Am I overthinking this, or is there really a difference I should know of?

Solution 1:

1. The definitions of credit and accredit clearly overlap at acknowledging the role of another. The semantic overlap:

credit
verb (credits, crediting, credited)

[WITH OBJECT]
1.0 Publicly acknowledge a contributor’s role in the production of (something published or broadcast):
the screenplay is credited to one American and two Japanese writers

1.1 (credit someone with) Ascribe (an achievement or good quality) to someone:
he is credited with painting one hundred and twenty-five canvases

accredit
verb (accredits, accrediting, accredited)

[WITH OBJECT]
1.0 Give credit to (someone) for something:
he was accredited with being one of the world’s fastest sprinters

1.1 (accredit something to) Attribute an action, saying, or quality to:
the discovery of distillation is usually accredited to the Arabs

ODO Emphasis mine

The semantic similarities are reinforced by the syntactical similarities:

1. The work is credited to the person, and the work is accredited to the person

2. The person is credited with the work, and the person is accredited with the work.

2. The words credit and accredit have each expanded separately into different uses. Credit dominates financial contexts, while accredit dominates authorization contexts:

credit

2.0 Add (an amount of money) to an account: this deferred tax can be credited to the profit and loss account
3.0 [OFTEN WITH MODAL] British Believe (something surprising or unlikely): you would hardly credit it—but it was true

accredit
2.0 (Of an official body) give authority or sanction to (someone or something) when recognized standards have been met:
institutions that do not meet the standards will not be accredited for teacher training
(as adjective accredited) an accredited practitioner

3.0 Give official authorization for (someone, typically a diplomat or journalist) to be in a particular place or to hold a particular post:
no journalist accredited to the UN has ever been expelled

3. By loose association with its numerous noun form uses, credit tends to be a more general term than accredit. Credit entered English from French in the early 16th century as a noun and then extended into use as a verb:

n.
1520s, from Middle French crédit (15c.) "belief, trust,"
from Italian credito,
from Latin creditum "a loan, thing entrusted to another,"
from past participle of credere "to trust, entrust, believe" (see credo).
The commercial sense was the original one in English (creditor is mid-15c.).
Meaning "honor, acknowledgment of merit," is from c. 1600.
Academic sense of "point for completing a course of study" is 1904.
Movie/broadcasting sense is 1914.
Credit rating is from 1958;
credit union is 1881, American English.

v. 1540s, from credit (n.). Related: Credited; crediting.

etymonline.com

Accredit entered English directly as a verb about 70 years after credit began extending to its verbal use:

1610s, from French accréditer, from à "to" (see ad-) + créditer "to credit" (someone with a sum), from crédit "credit" (see credit (n.)).

etymonline.com

Solution 2:

Credit generally refers to the definition you gave. The definition you found for accredit is a secondary one, though. Accredit is generally used in a different context, to mean: "to give official authorization to or approval of". See Merriam's definitions for accredit:

1. to give official authorization to or approval of
2. to give recognition to (someone or something) for doing something

Both are valid, but the first is more common. The second is equivalent to credit.