I've always thought that there is a generic, "family" resemblance between a number of bass marques that were around in the early 80s, close enough that I always felt that there was a lot of borrowing going on.
I agree that there's a long list of detailed differences between the Bass Collection and the SR range, yet the overall look & feel is remarkably similar. There was also a range by (I think) Yamaha at the same time, plus of course the early Tune basses, and I'm sure there were others I haven't mentioned.
My guess would be that someone came up with an overall design that worked really well and which wasn't yet another Fender clone, and a bunch of manufacturers fell into line behind it.
All these basses were (I believe) lighter than their Fender equivalents, the bar being set lower by Fender's back-crushing output in the late 70s. I wonder if this has anything to do with the pro-Fender (and others) propaganda that then started to emerge about how heavier basses always and automatically sounded better than lighter basses.