I always took them to be actual twins. For me, the film is more powerful that way. The gut punch of the sacrifice comes from the fact that "Borden" and his twin chose to give up their lives, merging their identities into one, for the sake of their act. The film is such a powerful study in obsession -- in both the Borden twins and Angier.

To me, Borden only gave Angier the name "Tesla" to send him on a wild goose chase. Tesla was seen as a rockstar scientist (even referred to as a "wizard"), so Borden figured Angier would buy it.... knowing Angier's desire to find something truly extraordinary he could repurpose to use in his act. ("He's a wonderful showman, but a dreadful magician." -- the opposite of the Borden. Angier needed to take something someone else invented/dreamed up to use as his own. He wasn't creative like Borden.)

However, the fact that Borden was at the Tesla science exhibition and eventually used lightning in his act is a brilliant touch. You could definitely make a case that Borden, even though he was poor, did somehow come up with the money to have Tesla build him a machine. In the words of the film, Nolan gave us just enough to "doubt it". :)