Etymology question to these three expressions:
We know Joseph could have been accused of "criminal conversation" which was a cause of action by a wronged spouse against his wife's seducer.
But Joseph also admitted to the other types of conversation-- trifling- and unchaste conversation.

Here's the question to legal history scholars: is "unchaste conversation" related to "criminal conversation" such as fornication is related to adultery.

From Joseph's 1834 letter to Oliver:
" At the age of ten my father’s family remo ved to Palmyra, N.Y. where, and in the vi cinity of which, I lived, or, made it my place of residence, until I was twenty one—the lat ter part, in the town of Manchester.
During this time, as is common to most, or all youths, I fell into many vices and fol lies; but as my accusers are, and have been forward to accuse me of being guilty of gross and outragious violations of the peace and good order of the community, I take the oc casion to remark, that, though, as I have said above, “as is common to most, or all youths, I fell into many vices and follies,” I have not, neither can it be sustained, in truth, been guilty of wronging or injuring any man or society of men; and those imperfections to which I alude, and for which I have often had occasion to lament, were a light, and too often, vain mind, exhibiting a foolish and tri fling conversation.
This being all, and the worst, that my ac cusers can substantiate against my moral character, I wish to add, that it is not with out a deep feeling of regret that I am thus called upon in answer to my own conscience, to fulfill a duty I owe to myself, as well as to the cause of truth, in making this public confession of my former uncircumspect walk, and unchaste conversation: and more partic ularly, as I often acted in violation of those holy precepts which I knew came from God. But as the “Articles and Covenants” of this church are plain upon this particular point, I do not deem it important to proceed fur ther. I only add, that I do not, nor never have, pretended to be any other than a man “subject to passion,” and liable, without the assisting grace of the Savior, to deviate from that perfect path in which all men are com manded to walk!"

Hmm. Criminal conversation is seducing a woman, typically a married man seducing another man's wife, for adulterous purposes.

Unchaste conversation is engaging in lewd and unchaste behavior (making out, feeling up, up to and including sexual intercourse) with a single woman. Could it also be sex with a prostitute? He does say he never claimed to be anything but subject to passion--though I am not sure if passion here just means being too full of strong feeling and inappropriately exhibiting high spirits, or actual passion as in love or sex.

Trifling conversation here seems to mean just that: talking about nothing serious, mature or substantial. Maybe he is saying he talked about made up things, ie: the supernatural skill he said he possessed to find buried treasure, or magik, as in using peep stones to do the same, and that he lied about them? Or just that he spoke about things a prophet should not concern himself with, like beauty/looks, clothes, money, women, or other material or worldly things...

Uncircumspect walk usually means professing to be a Christian but not attending church, reading scripture, or keeping the Sabbath holy. In general, being unworthy and behaving unlike a decent, Christian young man should do, as regards his faith and his regular worship of God and Jesus Christ. It could also mean he's admitting to being a con man here, but I doubt it. I think he puts/rolls that in under the vain and foolish part of his letter, and also under "in violation of those holy precepts which I knew came from God"...

"Vices and follies" could be drinking, using tobacco, swearing or gambling with dice or cards.

I could not find a legal definition for "unchaste conversation."

Where Smith originally wrote:
I was left to all kinds of temptations, and mingling with all kinds of society, I frequently fell into many foolish errors and displayed the weakness of youth and the corruption of human nature, which I am sorry to say led me into divers temptations, to the gratification of many appetites offensive in the sight of God.[7]

it could mean "unchaste conversation" which was edited to levity:
[7]Times and Seasons 3, no. 11 (April 1, 1842):749; cf. JS-History 1:28. The following words were added after the publication of the above: "In making this confession, no one need suppose me guilty of any great or malignant sins: a disposition to commit such was never in my nature; but I was guilty of Levity, & sometimes associated with Jovial company &c, not consistent with that character which ought to be maintained by one who was called of God as I had been; but this will not seem very strange to any one who recollects my youth & is acquainted with my native cheery Temperament." Manuscript History of the Church, Book A-1:133, note C, LDS Church History Library, Salt Lake City, Utah, added in December 1842, written by Willard Richards.

Maybe he really meant levity with double meaning.