Mmm white tigers are different from albino tigers, I think it is vital to point out. You're right, albino tigers would be all white with red eyes, but the gene that makes white tigers white merely deals with the orange part, leaving the stripes. White tigers are also not a different species or a sub-species anymore than blue eyed Caucasian people are different from brown eyed Caucasian people. Its a recessive gene, and white tigers don't give birth to exclusively white tigers or anything like that, they give birth to orange tigers as well. It merely is a rare gene trait, one that both Bengal, Siberian and possibly the other members of the tiger family have as well.
Plus, this information is all on Wikipedia, I found and absorbed in like five minutes. Gotta love Wiki.