A barrier above the current price is an up barrier, and one below it is a down barrier. Combined with knock-outs, which disappear when the barrier is touched, and knock-ins, which come into existence when it is touched, there are four types each for calls and puts. A knock-out that reaches expiry without touching the barrier pays the same as a standard option with the same strike price and expiry.
If you hold both a knock-in and a knock-out that can be exercised only at expiry and have the same terms, one of them remains as a standard option whether or not the barrier is touched. So without a rebate, the sum of their prices equals the price of the standard option (in-out parity).