I think, from looking at the meager sources, that a distinction into two kinds can be put forward for the elite troops of Gondor.

Earnur had an escort of knights when he rode to Minas Morgul, Imrahil had his Swan-Knights who were carefully made distinct from his other troops. The Stewards had their Tower Guards, and Faramir was given a "Guard" unit when he was invested with his principality.

I would submit that Gondorian potentates (kings, stewards and princes) had two classes of "Household" troops differentiated by professional status and social status. Firstly they had guards, composed of fully professional soldiers, probably chosen from the standing army from troops who had shown particular prowess or loyalty. I suspect that these troops normally operated as heavy cavalry in the field, but had the ability to fight on foot as well. Secondly they seem to have had "Household knights" whose major distinction was probably social. Drawn from the social elite of a particular region I imagine these to have been a semi-professional corps. This, in times of peace, probably consisted of the young unmarried members of the nobility, maintained within the king's or prince's household as a readily available body of elite heavy cavalry made formidable by their elan and knightly brotherhood. In times of war this group could be readily expanded by former members, who had married and succeded to estates, returning to their unit for a specific campaign.

In Imrahil's case the Swan-Knights would be the household knights of the prince, consisting of the young nobility and gentry of Belfalas. The seven hundred men-at-arms would be the Dol Amroth Guard, the equivalent of the Tower Guard of the Stewards and the Guard of Faramir as Prince of Ithilien.