Osgiliath was the great city of Gondor in the days of its splendour.
Osgiliath is Sindarin, ost = citadel or fortress and giliath = stars, so Osgiliath = citadel of the stars.
Elostirion is the name of the tallest and most western tower on Emyn Beraid, the Tower Hills to the West of the Shire.
Elostirion is Quenya, and shares the same root as palantír , tir = 'to look at (towards), watch, watch over'. In the proper name of the tower this root takes the form tirion, Quenya 'Watch-tower'. (Source: The Road Goes Ever On)
But what about the 'elos'? Online, I find:
But here is the thing. The early drafts of LotR in The War of the Ring reveal that in 1944 Elostirion was actually the name of the great city in Gondor.The -tirion of Elostirion's name can be safely interpreted as 'watchtower' (in a special sense that it held the Elendil Stone, which granted a view of Tol Eressëa in the lost West). The el- element is either 'Elf' or 'star' (with 'Elf' more likely, as the towers of the Tower Hills are elsewhere called 'Elf-towers'). Finally the connecting -os- typically refers to walled or fortified buildings or cities, hinting that the tower was protected by its own encircling wall.
At this moment, Tolkien had not given thought to the Seeing Stones in the North, the three Elf-towers of Emyn Beraid had yet to be associated with them, and the tallest was not yet named. And at this point the 'masterstone' of the 7 was said to have been housed in (what is now) Osgiliath, what had before in the drafts been named Osgiliath, but now Tolkien was naming Elostirion.
This is boiling my brain and any linguistic (or other) thoughts would be appreciated.