"The result of kamma is of three sorts, I tell you" - Are the "sorts" explicated anywhere in the canon?

This standard formula on divine eye appears frequently. Both karma, and rebirth are intertwined (both showing effects of right or wrong view and action), and the same phrase OP is questioning, reappearing in the next life (upapajjati), is used in this formula and indubitably means rebirth.

Dibbena cakkhunā visuddhena atikkantamānusakena satte passati cavamāne upapajjamāne hīne paṇīte suvaṇṇe dubbaṇṇe, sugate duggate yathākammūpage satte pajānāti: ‘ime vata bhonto sattā kāyaduccaritena samannāgatā vacīduccaritena samannāgatā manoduccaritena samannāgatā ariyānaṃ upavādakā micchādiṭṭhikā micchādiṭṭhikammasamādānā, te kāyassa bhedā paraṃ maraṇā apāyaṃ duggatiṃ vinipātaṃ nirayaṃ upapannā. Ime vā pana bhonto sattā kāyasucaritena samannāgatā vacīsucaritena samannāgatā manosucaritena samannāgatā ariyānaṃ anupavādakā sammādiṭṭhikā sammādiṭṭhikammasamādānā, te kāyassa bhedā paraṃ maraṇā sugatiṃ saggaṃ lokaṃ upapannā’ti. Iti dibbena cakkhunā visuddhena atikkantamānusakena satte passati cavamāne upapajjamāne hīne paṇīte suvaṇṇe dubbaṇṇe, sugate duggate yathākammūpage satte pajānāti.

With clairvoyance that is purified and superhuman, they see sentient beings passing away and being reborn—inferior and superior, beautiful and ugly, in a good place or a bad place. They understand how sentient beings are reborn according to their deeds: ‘These dear beings did bad things by way of body, speech, and mind. They spoke ill of the noble ones; they had wrong view; and they acted out of that wrong view. When their body breaks up, after death, they’re reborn in a place of loss, a bad place, the underworld, hell. These dear beings, however, did good things by way of body, speech, and mind. They never spoke ill of the noble ones; they had right view; and they acted out of that right view. When their body breaks up, after death, they’re reborn in a good place, a heavenly realm.’ And so, with clairvoyance that is purified and superhuman, they see sentient beings passing away and being reborn—inferior and superior, beautiful and ugly, in a good place or a bad place. They understand how sentient beings are reborn according to their deeds.

AN 3.58

there is similar structure regarding the results in MN 136.

"Now there is the person who has killed living beings here... has had wrong view. And on the dissolution of the body, after death, he reappears in a happy destination, in the heavenly world. But (perhaps) the good kamma producing his happiness was done by him earlier, or the good kamma producing his happiness was done by him later, or right view was undertaken and completed by him at the time of his death. And that was why, on the dissolution of the body, after death, he reappeared in a happy destination, in the heavenly world. But since he has killed living beings here... has had wrong view, he will feel the result of that here and now, or in his next rebirth, or in some subsequent existence.

"Now there is the person who has abstained from killing living beings here... has had right view. And on the dissolution of the body, after death, he reappears in a happy destination, in the heavenly world. But (perhaps) the good kamma producing his happiness was done by him earlier, or the good kamma producing his happiness was done by him later, or right view was undertaken and completed by him at the time of his death. And that was why, on the dissolution of the body, after death, he reappeared in a happy destination, in the heavenly world. But since he has abstained from killing living beings here... has had right view, he will feel the result of that here and now, or in his next rebirth, or in some subsequent existence.
MN 136

For more information about the mechanics of karma, I would investigate storehouse consciousness.

After reading an answer to another question - which references AN 4.77 - on this forum, I would perhaps advise with caution when investigating the precise workings of karma.

"The [precise working out of the] results of kamma is an unconjecturable that is not to be conjectured about, that would bring madness & vexation to anyone who conjectured about it."
AN 4.77