Are "Yet" and "However" synonymous?

Crabb's Synonymes [sic] has the following entry which explains the difference between these synonymous terms:

However, Yet, Nevertheless, Notwithstanding.

These conjunctions are in grammar termed adversative, because they join sentences together that stand more or less in opposition to each other.

However is the most general and indefinite; it serves as a conclusive deduction drawn from the whole. "The truth is, however, not yet all come out"; by this is understood that much of the truth has been told, and much yet remains to be told: so likewise in similar sentences, "I am not, however, of that opinion"; where it is implied either that many hold the opinion or much may be said of it, but, be that as it may, I am not of that opinion: "however, you may rely on my assistance to that amount"; that is, at all events, let whatever happen, you may rely on so much of my assistance: however, as is obvious from the above examples, connects not only one single proposition, but many propositions either expressed or understood.

Yet, nevertheless, and notwithstanding are mostly employed to set two specific propositions either in contrast or direct opposition to each other; the latter two are but species of the former, pointing out the opposition in a more specific manner. There are cases in which yet is peculiarly proper, others in which nevertheless, and others in which notwithstanding are preferable.

Yet bespeaks a simple contrast; "Addison was not a good speaker, yet he was an admirable writer; Johnson was a man of uncouth manners, yet he had a good heart and a sound head"; nevertheless and notwithstanding could not in these cases have been substituted.

Nevertheless and notwithstanding are mostly used to imply effects or consequences opposite to what might naturally be expected to result. "He has acted an unworthy part, nevertheless I will be a friend to him as far as I can"; that is, although he has acted an unworthy part, I will be no less his friend as far as lies in my power.

"Notwithstanding all I have said, he still persists in his own imprudent conduct; that is, all I have said notwithstanding or not restraining him from it, he still persists. "He is still rich, notwithstanding his loss"; that is, his loss notwithstanding, or not standing in the way of it, he is still rich. From this resolution of the terms, more than from any specific rule, we may judge of their distinct applications, and clearly perceive that in such cases as those above cited the conjunctions nevertheless and notwithstanding could not be substituted for each other, nor yet for either: in other cases, however, where the objects are less definitely pointed out, they may be used indifferently. "The Jesuits piqued themselves always upon their strict morality, and yet [notwithstanding or nevertheless] they admitted of many things not altogether consonant with moral principle. You know that these are but tales, yet [notwithstanding, nevertheless] you believe them."