I recently obtained a Global Entry card and on the back is the PASSID number that I understand is also my Known Traveler Number. When I recently tried to record my KTN with an airlines it asked for both a Redress Control Number and a KTN. My question is: does one need both to qualify for TSA PreCheck?
No you do not. A Known Traveler Number is for PreCheck. You can get into PreCheck via a number of programs, including Nexus. For Nexus people, put your PASSID (from the back of your card) into the Known Traveler Number field.
A redress number is like an override if your name is on the Do Not Fly. Most of us don't have them. But people with the same name as someone on DNF can apply to have their problem (that they can't fly) redressed, and at the end of that process they get a redress number, that they have to enter everywhere so that they can fly. TSA explains this. So does Air Canada. Should you have one, you will have to enter it here, just as you enter it all kinds of places like checking in online. If you don't have one, leave the field blank and ignore it. See also What's a "Redress Control Number"?
Global entry gets you PreCheck. There are more details at TSA.gov
From the link: Global entry members are eligible to participate in TSA Precheck Logo. U.S. citizens and lawful permanent residents enrolled in NEXUS or SENTRI are also eligible to participate in TSA Precheck Logo, as well as Canadian citizens who are members of NEXUS.
How It Works
If you are a Global Entry member or eligible NEXUS or SENTRI member, enter your membership number (PASS ID) in the “Known Traveler Number” field when booking reservations, or enter it into your frequent flyer profile with the airline. The membership number enables Transportation Security Administration’s (TSA) Secure Flight System to verify that you are a legitimate CBP Trusted Traveler and eligible to participate in TSA Precheck Logo.