No problem!
Alexander NY's, Vandoren V16's, Rico Orange Box. American cut reeds are generally a flatter profile reed with a thicker end, as distinct from a Classical Cut (such as Rico Royal, Vandoren Blue Box) which are thicker at the start and go very thin at the tip. The Jazz Cut is somewhere in between so starts off flatter than the classical cut but ends thinner than the American cut, so is generally the most flexible reed.
Hope this helps. The American Cut is especially suited to mouthpieces with a long facing curve where flexibility may badly affect playing by closing the reed on the mouthpiece. The Classical cut is more suited to shorter facings and the Jazz more suitable for medium facing curves, though many folks adapt comfortably to the combination that they adopt, whatever it is. Recently I've been playing a Phil-Tone Equinox mouthpiece (longer facing)on my Tenor Sax and the NY reeds sound much better than my Marca Jazz reeds, even though they are the same hardness.
Kind regards
Tom
Having looked at what is online there is the main distinction between American Cut and French Cut. I would say that French Cut is almost the same as a Classical Cut. The Jazz Cut is almost described as a Filed reed (reeds CAN be Filed or Unfiled - the NY and V16 are unfiled), which can be either an American Cut (such as Alexander DC - Double Cut, or Rico Jazz Select Filed) or possibly a French Cut reed which has been filed.