If the CD is in a tax-deferred or tax-free account, such as an IRA or Roth IRA, interest on the CD is not currently taxed; the rollover of the CD when it matures is not a taxable event. If the CD is in a taxable account, interest is taxable, but again rolling over the proceeds when the CD matures is not a taxable event.
The difference between face value of a bond and lower market price, attributable to rising interest rates. On a sale, gain on the bond is generally taxed as ordinary income to the extent of the discount.