I've had both & I think I've noticed the differences. Basically the receiver directly in front of the bolt handle (like the bridge where the rear scope mount sits) is shorter along with the tang.
Far as I know, that's it. After owning both, I prefer the Seven. But there's less cool stuff like peep sights & detachable mag conversions for it if you're into that kinda stuff.
The receivers are different diameters, the bolts are different diameters, the barrel threads are different diameters, the triggers are similar but different. The list goes on. Other than the obvious superficial similarities, they are different actions. But they are both very nice actions.
I actually own a older walnut stocked Model 7 in 223. Anyway the only subtle difference's between the two actions I've noticed are three key items. The dia/size and length of their barrels. Again their trigger works may differ some also. My model 7 came with barrel sights. Model 7 is a short light weight rifle. I don't think the s/a model 700 can claim the same.
You can have my little Model 7 when you pry it from my cold, dead hands. I love that little thing. It just seems so much more pleasant to carry in the field when compared to a full-sized rifle.
The 7 is the shorter, lighter action, but with a larger loading/ejection port. To do this there is far less metal on the rear receiver bridge. Original 7's only had 1 hole drilled on the rear bridge meaning 1 piece base pretty much had to be used. More recent 7's have 2 holes very close together opening up more scope mounting options.
The 7 is the prefered choice for a true lightweight hunting rifle. The SA 700 action is stiffer and probably the better choice for a true target rifle. There are far more options for aftermarket parts for the 700 as well.
Personally the 2-3 oz weight difference is not worth the negatives to me. Between the 2 I'd opt for the SA 700.