OK, I can see that it might be confusing. Fullerton could technically refer to anything made at the Fullerton plant before it closed early in 1985.
In practice, when people talk about Fullerton Strats, they usually (in my experience) mean one of the early US 57RI or 62RI models, & that's what I mean. Fender first produced accurate (with a few minor details "wrong" such as dot spacing) re-issues of 57 & 62 Strats in 1982, shortly after the Fender Japan range became available. As we all know, it was the Springy which showed Fender the way - in 1978 to 1982 the best "vintage Strat" you could buy was a Springy.
They made them from late 1982 till very early 1985, when CBS sold Fender, but not the Fullerton plant, which closed. In late 1985 the new Corona plant opened, & the first guitars made there (in 1986 - I'm not sure if any were made in 85) were RI Strats made from left over Fullerton bits. I know this is true as the body contours were different on the Fullerton models, & I have an 86 which has the same contours. There were few staff and few guitars made in 1986 - most Fenders sold at this time were MIJ.
The 82 to 84 Fullertons are highly sought after, much as the JVs are, & I regard them as very special guitars. Although some people deny this, I am convinced that the early USRIs are all nitro - there is no sign of any sort of poly base coat, & they wear & check just like a real 62 would, except that they are 20 years newer. They sell for a lot of money now, just as many JVs do, & many people question if they are overpriced. I reckon they are the next great collectible Fenders after the pre 65 stuff - they are easily much better instruments than the 70s stuff, & the prices reflect this.
So, that's what I mean by a Fullerton. Incidentally, the necks on the early 62RIs are about as slim as any Strat necks I've ever tried, which is just what I love. A bit like a RW board Goldstar, but with a soft and thin nitro finish. If any Strat lover has a chance to try an 82 to 86 USRI, I would advise you to grab the chance, so you can make your own assessment of what they are like.
Hope this helps.