The difference between karet and ibud

Usually, when Hashem specifies a Divinely-imposed punishment, it is kares. Yet, in Vayikra 23:30, there is a seemingly different punishment:

כט  כִּי כָל-הַנֶּפֶשׁ אֲשֶׁר לֹא-תְעֻנֶּה, בְּעֶצֶם הַיּוֹם הַזֶּה--וְנִכְרְתָה, מֵעַמֶּיהָ.	29 For whatsoever soul it be that shall not be afflicted in that same day, he shall be cut off from his people.
ל  וְכָל-הַנֶּפֶשׁ, אֲשֶׁר תַּעֲשֶׂה כָּל-מְלָאכָה, בְּעֶצֶם, הַיּוֹם הַזֶּה--וְהַאֲבַדְתִּי אֶת-הַנֶּפֶשׁ הַהִוא, מִקֶּרֶב עַמָּהּ.	30 And whatsoever soul it be that doeth any manner of work in that same day, that soul will I destroy from among his people.

What is the difference between these two, between וְנִכְרְתָה and וְהַאֲבַדְתִּי? In either case, it seems that it is imposed upon הַנֶּפֶשׁ. Though nefesh might mean "soul", or might mean "person", "individual".

Rashi gives the following explanation:

I will destroy: כָּרֵת (“excision” or “cutting off”) is stated [as a punishment] in many places [in Scripture] and I do not know what that means, when God says [explicitly] “I will destroy,” [coinciding with וְנִכְרְתָה in the preceding verse,] this teaches us כָּרֵת means only “destruction” [i.e., premature death, and not that the body is to be cut up or that the person is to be exiled]. — [See Be’er Basadeh on this verse and on 22:3 above; Torath Kohanim 23:180]

והאבדתי: לפי שהוא אומר כרת בכל מקום ואיני יודע מה הוא, כשהוא אומר והאבדתי, למד על הכרת שאינו אלא אבדן:

As noted in the translation, Rashi pulls this from Torat Kohanim:

כי כל הנפש אשר לא תעונה בעצם היום הזה

ונכרתה הרי זו עונש עינוי. והאבדתי מה

תלמוד לומר לפי שהוא אומר כרת בכל מקום

ואיני יודע מהו. כשהוא אומר והאבדתי לימד

על הכרת שאין אלא אבדן.

This makes sense, on a peshat level. See how a phrase is used in similar context, and assume that one is a synonym for the other. Do not assume that slight variance in word-choice means that a completely different punishment is in play.

Despite Rashi saying it, and despite it being a matter of theology encoded by Chazal, Ibn Ezra does not agree with this conflation in terms in order to arrive at a definition of the one. Thus,

כג, ל]
והאבדתי -
יש הפרש בינו ובין ונכרתה ולא אוכל לפרש.

That is, there is in fact a difference between the two. But he is unable to explain it.

I am not certain what Ibn Ezra means that he is unable to explain it. He could mean one of two possible things. Either that he does not know the difference, but is certain that there is a difference. Or, he could mean that he knows the difference, but since this is a deep spiritual matter, he is unable to explain the difference to his readers, the uninitiated. Either seems possible to me.

Ibn Caspi, though, feels himself perfectly capable of explaining the difference. He writes:

וכל הנפש אשר תעשה כל מלאכה . היטיב א"ע במה
שאמר: יש הפרש בין ונכרתה ובין והאבדתי ולא אוכל לפרש. ואמת
כי העירו בזה להיות שני אלו הפסוקים סמוכים והבדיל ביניהם ואמר
על הפורע הענוי עונש כרת, ועל העושה מלאכה עונש איבוד, וכבר
התבאר כי כרת הוא המחת זרעו ושמו, וזה עונש גופני, והאבוד חמור

מזה, ובלי ספק ראוי שיהיה עונש העושה מלאכה יותר חמור:

That is, Ibn Ezra writes well, and there is indeed a distinction between these two. And still, it is correct that these two pesukim are juxtaposed, and yet that there is a distinction between them. The one who does not practice inui on Yom Kippur gets the punishment of karet, and this was already explained as a destruction of his lineage and his name, and this is a physical punishment. And אבוד is more severe than this; and without a doubt it is appropriate that the punishment of one who performs labor should be more severe.

Ibn Caspi does not specify just what this more severe punishment is. But in stressing that kareis is physical, gufani, the implication seems to be that אבוד is spiritual. (See Ibn Caspi earlier on karet and ibud, though.)

And just what is kareis? (See Sanhedrin 64b, and varying levels.) There are a number of possibilities. It could be cutting off, as in early death. (Say, before age 60.) It could be cutting off descendants. It could be some spiritual punishment, such that the soul is severed, distanced, from Hashem, after death. It could be destruction of the soul, such that it ceases to exist. Or it could be some combination of these, or something else entirely.

Conflating the terms allows for extreme definitions of karet. Dividing the terms allows for general karet to be less severe. For example, Ibn Caspi regards karet as a physical punishment, and ibud as something more severe. This might be more extreme physically, or likely spiritually. Ibn Ezra makes a distinction, but does not outlay precisely what. If so, karet might be spiritual, as well. Given that ibud is the name of the more severe, and given that some medieval Rishonim (I am thinking Rambam and Ramban) discussed the utter destruction of the soul, the distinction might be between punishment and destruction.

I see now that a short while ago, on Hirhurim, Rabbi Gil Student discussed several medieval Jewish conceptions of kareit. See his post. This intersects with the discussion above.