So Sears had multiple card deals over the years. Infamously, Sears made Discover. Then when they spun Discover off, they got back into direct credit card lending themselves in the 90s, with the Sears Gold Mastercard introduced in 2001. Then when that wasn't helping their fortunes they
decided to get out of the credit card business and sell the MasterCard business off to Citibank by 2003.
Meanwhile, Kmart launched a card with HSBC in 2004. This of course predated the Kmart merger in 2005. So Sears announced
they were terminating their deal with HSBC and bringing the Kmart credit cards in under Citibank.
Fun fact that was apparently before my time: Sears used to allow paying of Discover card bills in Sears stores! Even though Sears spun off Discover in the 90s, this remained possible into at least the 2010s (
per this reddit /r/personalfinance post). Sears also allowed the Sears and Kmart cards to be allowed to pay themselves down without a fee, while still awarding 1% cashback on purchases - yes, this means exactly what you thought it means (it was possible to rack up a balance and then use one credit card to pay the other at the opposing store and have a negative 1% declining balance.)
The Shop Your Way card was a new deal and
the existing Sears Mastercard cardholders were offered the opportunity to link SYW accounts to get the 5-3-2-1 structure free through Dec 31, 2017.
Feb 2017 press release says that cardholders who opted in would start getting SYW branded cards in March 2017.
Anyways... there have been a variety of Citi credit card deals between Sears/Kmart/Kmart Holdings/Transformco (the survivor of the former companies after 2018 bankruptcy) over the years. Not every Sears or Sears Gold Mastercard holder was converted - my parent's Sears Gold Mastercard converted to a more generic Citi card earning ThankYou points probably circa 2018, but still with sears branding, and was converted to a Citi ThankYou card around May or March (can't remember) 2025 after they got a letter in the mail in Feb 2025.
These are likely Sears/Kmart legacy cardholders who were never migrated (or applied new) for the card to be converted/assigned anew as an SYW card, and thus Citi was able to convert them to be TYP sooner (and never offered the 5321 rewards structure, so no need to offer them anything so generous on the conversion, hence the "Citi ThankYou Mastercard", "ThankYou MasterCard for Select", and the Citi ThankYou Mastercard for Core" having different names and rewards tiers.)
The core maps to the SYW card. The other too, I'm not really sure - I'm too young and the internet isn't being kind in finding out the rewards structures of the older cards!
The Gold Mastercard used to get 5% cashback on gas/grocery/drugstores, capped at $300/yr max. That maps to the TYMC for Select, but not at the 5% rate (only 2%) - Sears/Citi probably nerfed it at some point.