Salamun Alaikum.
'Al-bayt' simply means 'the house', a particular structure (definite noun) for habitation or a place of worship. This can be a reference for the Kaaba or any other well known site of worship such as an ancient house.
'bayt' on its own (singularly) is an indefinite noun and simply means any house.
When 'al-bayt' (definite form) is referenced in the genitive, it obtains a kas'ra and becomes 'al-bayt-i'. In its accusative form it carries the fat'ha and reads 'al-bayt-a'. This is independent of whether the house in question is one at Makkah or elsewhere.
When ‘bayt’ (indefinite form) is referenced in the genitive, it becomes 'bayt-in'. In its accusative form it becomes 'bayt-an'.
Therefore:
Genitive Definite: (al-bayt-i) the house
Accusative Definite: (al-bayt-a) the house
Genitive Indefinite: (bayt-in) house
Accusative Indefinite: (bayt-an) house
If you note in 2:125 and 2:127, both references are to the house that Abraham built. But one has a 'fat-ha' and reads 'bayt-a' (in the accusative - 2:125) and the second has a kas'ra and reads 'bay-ti' (in the genitive - 2:127).
The Arabic language has three cases. (1) Nominative case (2) Genitive case and (3) Accusative case. The case is determined by the context and the syntax of where the noun appears. The case does not necessarily convey a separate meaning of its own.
I hope that helps, God willing.
Your brother in faith,
Joseph.