Captain of the Rangers of Ithilien
At the end of the twenty-ninth century of the Third Age of the Sun, Túrin II, the Ruling Steward of Gondor, decreed that a brotherhood of knights be formed in North Ithilien, as Gondor's power in that land was threatened by enemies from Mordor and Morgul. So the band called the Rangers of Ithilien was formed. This scouting-force of men were descended from those who lived in Ithilien before it was overrun. They were dressed in foresters' green, and fought with bows, spears and swords. After the War of the Ring, I would guess that many or all of them would have become the 'White Company', the Guard of Faramir.

→ "They were goodly men, pale-skinned, dark of hair, with grey eyes and faces sad and proud... Dúnedain of the South, men of the line of the Lords of Westernesse."
→ "They marvelled to see with what speed these green-clad men now moved, vanishing almost in the twinkling of an eye."

Captain of the White Tower
A military title. This duty was originally that of Boromir's, but after his death seems to have been taken up by Faramir. I guess that this is the title given to the man who leads (as apposed to Denethor, who only issues commands from the White Tower) Gondor's armed forces in battle. Presumably after the War of the Ring and Faramir's move to Ithilien, this title would have been passed on to one of Gondor's other captains.

→ "He leads now in all perilous ventures."

Steward of Gondor
Originally, this was the honorary title of the chief counsellor to the King of Gondor. In Michael Martinez' essay: The Men who would be Stewards (a worthy read on this particular subject), he describes them as "guardians, wardens, keeping an ancient trust placed in their hands by a family of kings... the Elvish word for "steward" is Arandur, 'King's servant.'" The title of 'Steward' became hereditary from the time of Steward Pelendur of the House of Húrin. After the loss of King Eärnur in Minas Morgul, Mardil became the first Ruling Steward, and his descendants ruled Gondor until Faramir surrended the rule to Aragorn.  However, Faramir retained the title of Steward. Tolkien is known to have noted "the chief commanders, under the King, would be Faramir and Imrahil: and one of these would normally remain a military commander at home in the King's absence." It is reported at least once in the appendices of the book that Elessar fought in foreign lands, so Faramir's position as Steward would indeed have remained active.

Prince of Ithilien
A royal title given to Faramir by King Elessar. He was rewarded with the province of Ithilien after the War of the Ring. The guard of Faramir established here was called the 'White Company' and Beregond was its Captain. Here is how Tolkien described this new responsibility set for Faramir: "Prince of Ithilien, the greatest noble after Dol Amroth in the revived Númenorean state of Gondor, soon to be of imperial power and prestige, was not a 'market-garden job'... Until much had been done by the restored King, the Prince of Ithilien would be the resident march-warden of Gondor, in its main eastward outpost - and also would have many duties in rehabilitating the lost territory, and of clearing it of outlaws and orc-remnants, not to speak of the dreadful vale of Minas Ithil (Morgul)." (Letters p323).

Lord of Emyn Arnen
A title presumably given to Faramir by the people of Ithilien; another version of 'Prince of Ithilien.' Emyn Arnen are the hills in Ithilien in which Faramir dwells in with his wife, Éowyn, and family after the War of the Ring. Húrin, the earliest of Gondor's Stewards to have his name recorded in history, came from these hills.