I just spent a delightful 5 hours racing down the rabbit hole that is Robert Messenger's OZ Typewriter, researching these machines, gathering a list of typewriter designers and the machines they designed, and impulsively following tangents. What a wonderful resource and an excellent way to pass the time recovering from the frustrating cough I picked up on vacation.
It appears that the Finger-Flite was Braginetz's first design for Underwood. Judging from TWDB, the Finger-Flite Champion & Universal replaced the William Dobson-designed Champion & Universal from 1936. I don't have a Dobson Champion to compare to my Finger-Flite to tell if this is just a re-skinning (likely), or more substantial.
The Deluxe was Braginetz's second design for Underwood, and judging by the TWDB, it replaced the Finger-Flite in 1953. I can't imagine them doing any significant changes under the hood. It looks like it's just a new ribbon cover and carriage.
In the end, I think the difference comes down to one designer evolving a design, as well as showing, given the only 3-4 year run of each machine before Olivetti took over, some of Underwood's desperation to compete in the portable market in the 50s...