Never done much research on bettas other than the common varieties. The last two seem to be quite different the fin rays for the yello betta are longer than those for the black one. Is it the same thing?
Both the yellow and the black/copper are Crowntails; however, the yellow CT is only a single-ray CT. The black/copper CT is a double-double ray (I believe that is what they are called) Crowntail.