The proposed gull-wing Seafire and the later Spitfire conversion

Is the Seafire proposed in this counterfactual the same aircraft as the wartime naval Spitfire?

No. The proposal discussed here is an earlier gull-wing naval fighter, distinguished from the later adapted Spitfire.

The name Seafire is used here for an earlier Supermarine naval-fighter proposal and for the later aircraft adapted from the Spitfire. The earlier design is described with a gull wing and a lower nose to improve carrier operation. Its development was stopped so that Supermarine could concentrate on the Spitfire, while the company continued supplying naval reconnaissance aircraft such as the Walrus. The proposed fighter is judged likely to sacrifice some straight-line speed for tighter turns. A compact footprint would allow eighteen fighters aboard an Illustrious alongside twenty-four strike aircraft, and a larger fuel provision would suit naval requirements.