So, to sum up, κάπρος occurs 15 times in the early hexameter corpus; in 7 instances it refers to a domestic (?) male boar, every time in the context of sacrifice, except once in Hesiod (WD 790, not 690 like I said earlier), where we’re dealing with castration. The combination σῦς κάπρος occurs 3 times and always refers to a wild boar, as do the remaining 5 instances of κάπρος alone. κάπριος occurs 4 times (twice joined with σῦς), and always means wild boar.
Having now taken a closer look at the passages, I now think that κάπρος applied to a domestic pig refers to an uncastrated male (domestic?) pig. Perhaps male σῦς without κάπρος (as in the Od. 14.414-439 passage) would then always be castrated? Looking at the passages where κάπρος refers to a domestic boar, it’s interesting to note that beside the Hesiod passage that refers to castration (an operation after which, if I’m correct, it ceases to be a κάπρος), we have 2 instances of domestic κάπρος explicitly in the function of a stud for breeding, συῶν ἐπιβήτορα κάπρον “boar that mounts [female] pigs”.
Beside these, we’re left with 4 instances of domestic κάπρος that have not been accounted for; they all occur in the same passage of Iliad 19; it’s funny, as mwh already noted, that the word ταμέειν “to cut” which means “to castrate” in the Hesiod passage is used here in 19.197 in the context of sacrifice – perhaps a “contamination” from castration formulas to a sacrificial passage (if you understand what I mean)? And it is to be noted that in 19.251 the herald Talthybios seems to hold the κάπρος with a single hand κάπρον ἔχων ἐν χειρὶ – indicative of a rather young boar, I’d say.
Here are all the occurrences of κάπρος for your reference:
IL.5.783 ἢ συσὶ κάπροισιν, τῶν τε σθένος οὐκ ἀλαπαδνόν,
IL.7.257 ἢ συσὶ κάπροισιν, τῶν τε σθένος οὐκ ἀλαπαδνόν.
IL.11.324 τὼ δ’ ἀν’ ὅμιλον ἰόντε κυδοίμεον, ὡς ὅτε κάπρω
IL.17.21 οὔτε συὸς κάπρου ὀλοόφρονος, οὗ τε μέγιστος
IL.17.725 ἴθυσαν δὲ κύνεσσιν ἐοικότες, οἵ τ’ ἐπὶ κάπρῳ
IL.19.197 κάπρον ἑτοιμασάτω ταμέειν Διΐ τ’ Ἠελίῳ τε.
IL.19.251 κάπρον ἔχων ἐν χειρὶ παρίστατο ποιμένι λαῶν.
IL.19.254 κάπρου ἀπὸ τρίχας ἀρξάμενος Διῒ χεῖρας ἀνασχὼν
IL.19.266 ἦ, καὶ ἀπὸ στόμαχον κάπρου τάμε νηλέϊ χαλκῷ.
OD.6.104 τερπομένη κάπροισι καὶ ὠκείῃς ἐλάφοισι:
OD.11.131 ἀρνειὸν ταῦρόν τε συῶν τ’ ἐπιβήτορα κάπρον,
OD.23.278 ἀρνειὸν ταῦρόν τε συῶν τ’ ἐπιβήτορα κάπρον,
WD.790 μηνὸς δ’ ὀγδοάτῃ κάπρον καὶ βοῦν ἐρίμυκον
SH.172 ἤδη γάρ σφιν ἔκειτο μέγας λῖς, ἀμφὶ δὲ κάπροι
SH.387 κάπρος χαυλιόδων φρονέει [δὲ] θυμῷ μαχέσασθαι