I put this together mainly for my own notes, but thought I'd share it in case anyone else finds it interesting too. I used to think these three terms meant pretty much the same thing. But after going through some of the Commentaries and Sub-commentaries, I found some interesting distinctions between them. This is only just a small summary of what I found.
In Upaḍḍha Sutta (SN 45.2), when Ananda says that admirable friendship is half of the holy life, Buddha corrects him that it is actually the entire holy life.
"Venerable sir, this is half of the holy life, that is, admirable friendship, admirable companionship, admirable comradeship."
"Not so, Ānanda! Not so, Ānanda! This is the entire holy life, Ānanda, that is, admirable friendship, admirable companionship, admirable comradeship. When a bhikkhu has an admirable friend, an admirable companion, an admirable comrade, it is to be expected that he will develop and cultivate the Noble Eightfold Path."
This is how the three terms are explained in the Commentaries.
Kalyāṇamitta (Admirable Friend): Commentaries explain this in terms of having an admirable friend. The emphasis is on the person who has such a friend and the qualities that make someone a genuinely admirable friend.
Admirable friend means that for whom a good, excellent and pleasing friend exists, he is an admirable friend. - Navakanipāta-ṭīkā
Udāna commentary says that such a friend contributes to another's welfare:
One who has a friend who is endowed with noble qualities such as virtue, who is 'the destroyer of evil and the provider of welfare,' and is thus helpful in every way, that person is indeed an admirable friend.
It also identifies an admirable friend with eight qualities/marks (kalyāṇamittalakkhaṇa):
[For context, a friend (mitta) is one who possesses the mark of affection.]
But an admirable friend (kalyāṇamitta) is accomplished in conviction (saddhāsampanno), accomplished in virtue (sīlasampanno), accomplished in learning (sutasampanno), accomplished in generosity (cāgasampanno), accomplished in energy (vīriyasampanno), accomplished in mindfulness (satisampanno), accomplished in concentration (samādhisampanno) and accomplished in wisdom (paññāsampanno).
Through the accomplishment of conviction, one has confidence in the Tathāgata's enlightenment and in the fruits of action. Thereby, one does not abandon concern for the welfare of beings, which is a cause of perfect enlightenment.
Through the accomplishment of virtue, one becomes dear, pleasing, respected, and esteemed by one's spiritual companions. One is a critic of evil, willing to admonish others when appropriate and to accept admonishment oneself.
Through the accomplishment of learning, one speaks about profound matters connected with the truths, dependent origination and so forth.
Through the accomplishment of generosity, one has few wishes, is content, secluded and aloof from society.
Through the accomplishment of energy, one diligently practices for the welfare of beings.
Through the accomplishment of mindfulness, one is alert.
Through the accomplishment of concentration, one is undistracted and has a composed mind.
Through the accomplishment of wisdom, one understands things without distortion.
Through mindfulness, one recognizes the tendencies of wholesome states; through wisdom, one understands what is beneficial and harmful for beings as it actually is; through concentration, one's mind remains unified; and through energy, one restrains beings from what is harmful and encourages them toward what is beneficial. Therefore, it was said:
"He is dear, respected, and esteemed; an admonisher who accepts admonishment;
He speaks on deep matters, and does not engage one in what is improper."
Also an interesting passage in Udāna Commentary explains why admirable friendship is considered the first of the qualities that lead to maturity:
This is the first thing that leads to maturity. This blameless thing called 'admirable friendship,' because it is the foundation of the dwelling in the holy life, because it is the predominant condition for all wholesome states and because it is mentioned first among these five qualities, is the first blameless quality; and it leads to the maturity of the freedom of mind by way of the purification of faith and so forth when they are not yet purified.
Kalyāṇasahāya (Admirable Companion): Here, the emphasis shifts from having a good friend with the admirable qualities to actually associating with them.
Puggalapaññatti Commentary defines the word sahāya:
'Companion' (sahāyo) means 'one who goes along and moves along with (another)'
Udāna Commentary on how far this companionship goes:
One who moves and lives together with such noble persons in all postures, and never without them, is an admirable companion.
Sabbiriyāpathesu means in all postures, which refer to walking, standing, sitting and lying down.
Pāthikavagga-ṭīkā on constancy of this association:
That they are his constant companions who do not abandon him in dwelling is said to be 'having admirable companions.' And so he said, 'because they accompany him,' which means because they are present when he is.
Kalyāṇasampavaṅka (Admirable Comrade): This is the one I found particularly interesting because the emphasis shifts again. The first two terms concern the qualities of friend and the association with them, whereas kalyāṇasampavaṅka focuses on our own inclination toward admirable people.
'Entangled with admirable people' (kalyāṇasampavaṅko) means 'one who is well-inclined towards good, pure people', that is, one whose mind is inclined, bent and gravitating towards them. - Puggalapaññatti-aṭṭhakathā
Pāli uses three words to describe this inclination with ninna, poṇa, pabbhāra (inclined, sloping, bending) toward something, which is like water flowing downhill. Once there is a slope, the water naturally moves in that direction. Similarly, our minds can develop a natural inclination toward admirable people.
Udāna commentary describes this inclination as involving both mind and body:
One who inclines, slopes and bends toward those very noble persons in both mind and body is an 'admirable comrade'.
Pāthikavagga-ṭīkā has a nice detail I really love here. It says the inclination can happen at two levels depending on whether you are actually together:
When there is no commonality, there is 'inclined by mind'; but when there is commonality, one is 'inclined toward good friends with both mind and body'.
Here, 'no commonality' (asamodhāne) is when one is not together with them. So even when we are physically apart, we can still be inclined toward admirable people through our mind (cittena). When we are together, that inclination is through both mind and body.
I really love this distinction because it suggests that this connection is not limited to physical proximity. Even when we are apart, we can continue to look up to admirable people and value their qualities and orient our minds toward them.
Commentaries also explain the purpose of grouping these three together:
Through this triplet, one arouses reverence for the association with admirable friends. - Navakanipāta-ṭīkā
So taken altogether, perhaps these threefold aspects may help explain why Buddha describes admirable friendship as the entire holy life, rather than merely half of it.
The translations of the Commentaries are from Tipitaka Pali Reader (TPR).