So seeing the two similar and one dissimilar endings here, I just checked out several words on Wiktionary.com, and I'll share my findings with y'all (but I also have questions). All of these words derive from feoil ("meat"):
— muc ("pig") + feoil -> muiceoil ("pork")
— mart ("ox or cow slaughtered for meat") + feoil -> mairteoil ("beef")
— lao (“calf”) + feoil -> laofheoil ("veal")
— fia (“deer”) + feoil -> fiafheoil ("(adult) venison")
— os (“deer”) + feoil -> oiseoil ("(fawn) venison")
— caora (“sheep”) + feoil -> caoireoil ("mutton")
— circe (“chicken, hen”) + feoil -> circeoil ("chicken (meat)")
These are straight-up compound words, right?
The Wiktionary says circe and circeoil are synonymous with sicín, and I'm guessing they're not transitively synonymous with each other, that circeoil is only for the butcher's block, and circe is the live bird. What's the frequency of sicín compared to circe & circeoil? Is this a regional thing?
Second, I'm noticing the spelling patterns in these compound words. It looks like feoil gets to keep its f when the root ends in a vowel, but it has to be lenited (laofheoil, fiafheoil). When the root ends in a consonant, an additional i might come in, and I'm guessing it's only after broad vowels (muiceoil, mairteoil, oiseoil, caoireoil) to force the consonant(s) into being slender. Is that right? I'm wondering are these 'i's silent?
circe is the genitive of cearc - "hen", so circeoil is "hen-meat", but just as the foodstuff is generally referred to as "chicken" in English, it has come to be referred to as sicín in Irish. It's not really a regional thing, it's just a different word that is used - some people consider it béarlachas.
The silent fh in many of these words disappeared in the spelling reforms of the 1950's. While they are obviously formed by joining two words together, they aren't like other "compound words", as the first part is modified by the addition a slender vowel if necessary, whereas leathan le leathan, caol le caol doesn't apply across the boundary in compound words like gluaisrothar or mótarbhealach.
As for pronunciation, the i in muiceoil definitely has an impact on the pronunciation of the first syllable.