What's the difference between "cozen" and "bamboozle"?

According to Oxford Dictionaries, cozen dates from the 16th century. Bamboozle dates from the 18th century and seems to be a humorous, slangy word. I don't think they necessarily have an official difference in meaning; there are other synonyms such as hoodwink, take in. I think of cozen as rather archaic.

Cozen is all but obsolete. In the past, it was used mainly to cover any form of deceit - it has been replaced by to cheat or fool (someone out of something/into doing something.) Usually the verb had negative connotations.

OED 1.a. transitive. To cheat, defraud by deceit.

1652 P. Heylyn Cosmographie ii. sig. Ss6v He that trusts to a Greek is sure to be cousened.

To bamboozle is current. It is not so negative. It tends to imply (i) that the deception was done by confusing the victim (ii) or simply that the person was tricked of fooled by confusion:

MW:

Bamboozle transitive

1 : to deceive by underhanded methods : dupe, hoodwink I got bamboozled by the salesperson to buy a more expensive model.

2 : to confuse, frustrate, ...

a quarterback bamboozled by an unexpected defense.