First to clarify or solidify what Peyton said, the 700 and the 770 are, design-wise, NOT related.
The 700 is a rifle/action that is considered a "Standard" in the rifle world and has a reputation for smoothness, quality, and in many guises above avergage accuracy.
the 770 is the "product improved" version 710 put out to compete with the likes of the low end Savages (stevens, and base savage). The original 710 wound up being a nightmare for Remington, more design flaws than I can count or remember. Including one that i never heard a full explaination for, something about a poor materials choice causing some sort of magnetic interference with the firing pin
the 710/770 was designed with price point in mind, not quliaty. as others have said it's acceptable in accuracy, mechanically functional, and cheap enough that if it happens to fail after 150-200 total rounds it's near disposable.
If, as has already been stated, you are looking for a rifle purely to hunt with once or twice a year and won't be shooting it on a regular basis, expect only "Minute of game animal" accuracy, and/or are looking for a pretty much disposable rifle, ie shoot it till it fails and then drop it in the nearest metal shredder and buy another/something better. then a 770 might actually be an OK rifle for you
consider the Marlin X7 or the Savage Axis (or even the Mossberg 100ATR) instead. Much better guns at similar prices.
While i was still working behind a gun counter, the absolute easiest way to get a customer who came in looking at a 770 to upgrade to
any of the above was to first hand them a 770, then hand them one of the guns above that sold for the same price or maybe $50-100 more.
Compared to pretty much all of it's competitors the Rem770
Feels like the POS it is. Especially to anyone who's owned or used a "real" remington (700, 600, 7 etc).