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Did Target send you a letter saying Equifax FICO score?
The scores on Equifax website are FAKO
OP, if you mean your score from myfico, it's a version called Beacon 5.0, that's commonly used for mortgage apps. The score commonly sold directly from the equifax site is indeed a fako.
I'm not familiar with the "redcard," so I don't know the fine points....(others that have it will jump in eventually).
It's possible that Target gave you either a card enhanced score, or an internal score, which means any past bad cc habits will affect it accordingly.