I would guess so. Is the C for "copyright"?
It might just be the copyright date for the artwork on the newer box.
Not sure about that, unless it was a different box than the two shown, I had the newer one (the top one) which I got christmas '87. (first game system I ever actually owned. Thought it was a NES before I opened it. Boy was I disappointed then, but now it's quite the opposite.) Unless of course, they updated the copyright on the box every year maybe? Or maybe just put '88 on that box because it was already almost '88.. who knows..I haven't seen that box in 20 years.. Looks like the bottom one was made back in '83 or '84 (considering the similarities to the 2600 and 5200 of the time), just maybe stocked in warehouses until the release or something.
I originally got a 7800 in 87 also, but I don't remember what box it had. The console itself was one of the earlier versions.
Whatever that mark on the box is, I doubt it has any strict connection to the console. I don't see much reason why they'd mark console production dates on the box.
Best way to get a build date would be to find some date codes on parts inside the console. That's still not exact, but you can assume it wasn't assembled much later than the latest date code you can find. In case anybody doesn't know how to read them - a code like 8732 would mean 32nd week of 1987.
If you don't want to take apart your console, look at the sticker on the bottom, in the box that says 'Serial Number' above it. For example, mine says 72R4BR A1 87 5406414 but the '7' in '87' is a slightly different color, like it was stamped on there. Since I got my 7800 in '87, I'm pretty positive that marking is to designate the year it was built.
(and the only reason I remember what box it was is because I remember sneaking into the living room while my parents were asleep and making a small tear to see what was under that paper..yeah I was a sneaky little bastard when I was a kid, but then again, who wasn't?)