This is Saint Patrick's Cathedral around 1908. Please note the completely different high altar, which was removed in the 1940's for a freestanding one under the Baldichino. This altar is attached to a reredos:
The oldest form of the altar of course is the free-standing one. The major basilicas in Rome all have historic free-standing altars. All of the major basilicas in Rome face east when the priest or bishop is celebrating Mass toward the nave, except for one, which is St. Paul's Outside the Walls. It altar faces St. Peter's and thus west, Saints Peter and Paul facing one another!
I prefer a free standing altar even if the older altar with its marvelous reredos remains in tact. It then become a back drop and place of reservation for the Holy Eucharist. This permits the Mass to be celebrated in either direction.
The Pauline Chapel at the Vatican renovated under the glorious reign of Pope Benedict has the table part of the altar detached from the main reredos, although it remains looking like one unit from the nave. Pope Benedict celebrated Mass on this altar ad orientem, Pope Francis has done so toward the nave. Either way is acceptable although I do have prejudice toward ad orientem for a variety of reasons, none of which are technically doctrinal.
This is Holy Innocents Church in Long Beach, California. The bishop there allowed an attached altar for it new construction. They also celebrate the other form of the one Latin Rite, the EF Mass: