Good question!
The terms here, as so often, are derived from the Brahmanical tradition. The meritorious offering to the Sangha is situated as a substitute for the kinds of offering that prevail in the brahmanical tradition. Essentially it is a dialectical passage, saying that the Sangha is as worthy or even more so, of offerings than these traditional forms of offering.
Āhuneyya is from the Vedic term āhuti, which is an oblation, typically of ghee or rice, poured into the fire as an offering for the gods. The notion that the offering to the Sangha is a rational replacement for this is spelled out in SN 6.3:
This sutta also mentions dakkhiṇa. The term dakkhiṇa also has a specific Vedic meaning: the offering or payment due to a teacher, specifically a brahmin, by their student. So the dakkhiṇa is an offering to a respected person, while the āhuti is an offering to the gods.
Over time, the Vedic sense of these words became lost, and were just read in the Buddhist community as generic terms for “offering”, etc. Most translators have translated them in this way. However, at the time of the Buddha, I believe, the Vedic context was very much alive. A generic translation, I felt, obscures the sense of the passage. There is a reason why these specific Vedic terms are used, rather than more generic terms like dāna, etc.