PaulMM (Overscan) said:
J101 was designated in the turbojet number sequence (J79, J97 etc). It was a USAF designation.
J101/SF was a scaled down F404 giving about 12,000lb thrust. It is possible the bypass ratio was reduced, as the PW1120 did from the F100, leading it to revert to the J101 designation.
According to the article, originally it was just a scaled fan version of the F404, hence the SF, but that ended up being 500 lbs too heavy. It states they then scaled the whole engine to make this one, but it has 80% parts commonality with the F404.