The two words occur several times together in the same verse, which is very helpful.
Even so every good (ἀγαθὸν) tree bringeth forth good (καλοὺς) fruit; but a corrupt tree bringeth forth evil fruit. A good (ἀγαθὸν) tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good (καλοὺς) fruit.
But that on the good (καλοὺς) ground are they, which in an honest (καλοὺς) and good (ἀγαθὸν) heart, having heard the word, keep it, and bring forth fruit with patience.
For I know that in me (that is, in my flesh,) dwelleth no good thing: (ἀγαθὸν) for to will is present with me; but how to perform that which is good (καλοὺς) I find not.
1 Timothy 5:10
Well reported of for good (καλοὺς) works; if she have brought up children, if she have lodged strangers, if she have washed the saints' feet, if she have relieved the afflicted, if she have diligently followed every good (ἀγαθὸν) work.
Looking at these verses, it can be seen that ἀγαθὸν refers to inner good (what is unseen, i.e within) and καλοὺς refers to outer good (what is seen, i.e. without). If you like, this is equivalent to the notion of unmanifest Tao and manifest Tao, or cause and effect.
So, yes. There are different concepts being expressed by the two words.
It seems, to some, that this idea is not so obvious, so let me draw a picture, and then elaborate further using the snippets Susan quoted.
ὥστε ὁ μὲν νόμος ἅγιος καὶ ἡ ἐντολὴ ἁγία καὶ δικαία καὶ ἀγαθή.
So the law is holy, and the commandment is holy and righteous and good.
The Law is ἀγαθή (a good tree - inside, at its core)
Τὸ οὖν ἀγαθὸν ἐμοὶ ἐγένετο θάνατος; μὴ γένοιτο·
Did that which is good, then, bring death to me? By no means!
Did the Law that is ἀγαθή (a good tree), bring death to me? Certainly not!
ἀλλ᾿ ἡ ἁμαρτία...διὰ τοῦ ἀγαθοῦ μοι κατεργαζομένη θάνατον...
It was sin, producing death in me through what is good ...
It was sin that brought death to me, which I recognise because I know the Law is ἀγαθοῦ (a good tree)
εἰ δὲ ὃ οὐ θέλω τοῦτο ποιῶ, σύμφημι τῷ νόμῳ ὅτι καλός.
Now if I do what I do not want, I agree with the law, that it is good.
Paul is now talking about DOING stuff, which is about FRUIT, i.e the outward product of the inward substance, and he recognises that the ἀγαθή Law should produce καλός fruit.
Οἶδα γὰρ ὅτι οὐκ οἰκεῖ ἐν ἐμοί, τοῦτ᾿ ἔστιν ἐν τῇ σαρκί μου, ἀγαθόν·
For I know that nothing good dwells in me, that is, in my flesh.
But it doesn't, because his flesh is not ἀγαθή, i.e. his flesh is not a (good tree) like the Law.
τὸ γὰρ θέλειν παράκειταί μοι, τὸ δὲ κατεργάζεσθαι τὸ καλὸν οὔ·
For I have the desire to do what is right, but not the ability to carry it out.
Paul is again referring to DOING stuff, so he's dealing with FRUIT, i.e. the outward product of the inward substance
οὐ γὰρ ὃ θέλω ποιῶ ἀγαθόν, ἀλλ᾿ ὃ οὐ θέλω⸃ κακὸν τοῦτο πράσσω.
I do not do the good I want, but the evil I do not want is what I keep on doing.
The fruit he produces is not in keeping with the ἀγαθόν Law.
εὑρίσκω ἄρα τὸν νόμον, τῷ θέλοντι ἐμοὶ ποιεῖν τὸ καλόν, ὅτι ἐμοὶ τὸ κακὸν παράκειται·
So I find it to be a law that when I want to do right, evil lies close at hand.
So, he has discovered a new law operating within himself: when he tries to produce the καλόν fruit that should result from the ἀγαθόν Law, evil is always near.
Of course, we know his conclusion on this matter: only God can rescue him from his body of death.