You are I’d say half-correct. F-20C was a proposed variant, but it never made it past the drawing board. The three existing/flying F-20s are as follows:
Prototype 1: Initially based on the F-5G ECO from the mid-late 1970s, being intended primarily for Taiwan as a point defense interceptor. For the actual aircraft: 16,000 lbf YF404-GE-100, aerodynamic improvements (shark nose, LERX, auto flap system), cockpit mostly the same as the F-5E. For the idea of the F-5G ECO, it would’ve also had a slightly modified APQ-159 with CWI and provisions for 2 Sparrows, but that’s about it. The actual first prototype first flew on August 30th, 1982, and shortly after was re-designated as “F-20A”. Prior to its first flight, the FX program had been initiated by President Carter, which is where Northrop sort of resurrected the idea for the F-5G but with heavy modifications to make to more comparable to the F-16A. The heavy modifications couldn’t be implemented on it, due to it mostly already being built.
Prototype 2: The first technically true F-20A, incorporating the changes meant for the FX program. These changes were: more powerful F404-GE-100 (17,000 lbf), re-designed nose to fit the APG-67 radar, heavily modified cockpit and panoramic canopy, and reduced ammunition for the twin 20mm cannons (from 560 rounds total to 460 total). Initially, Prototype 2 did not have the full avionics suite but would later be retrofitted with it. First flight was 1983.
Prototype 3: Technically the first fully production-esque Tigershark (until prototype 2 was retrofitted with the full avionics suite), pretty much the exact same specs as prototype 2. By the time this aircraft flew, Northrop already began investing in building the 4th prototype, as the intended “production” aircraft once again changed to to the F-20 now having to compete against the F-15, F/A-18, and F-16C on the export market.
When the Tigershark program was officially terminated in 1986 (I say officially due to Northrop attempting to bribe South Korea to license production of it sometime around 1988-1989), protos 1 and 2 were gone due to crashes, and only prototype 3 was left. The supposed prototype 4 had likely been scrapped.
With prototype 4 (frankly the whole topic of later F-20 models is a can of worms unto itself lmao), it had a number of major changes to actually make it more competitive, namely: larger 200 square foot wing and larger-span LERX, more powerful F404-GE-100A (18,000 lbf), APG-67 Extended Range radar in re-designed nose section, Wide-angle Heads-up Display, additional internal fuel tanks, and aerial refueling capability. I should point out that prototype 4 not only never flew due to being unfinished, but the actual uprated engine and extended range radar likely never existed, with only the proposals being the existing parts. Prototype 3 may have been fitted with the modified larger nose for its final few flights (aerodynamic testing purposes), but I can’t find really cohesive evidence of this.