Recording broadcast TV

I am a recent cord cutter, I use playstation vue for a few things, but there are others I receive over antenna.
With playstation vue I can use the service to record programming, but have no current way to do the same with antenna broadcasts.
Is the Rpi 2/3 powerful enough to do that with a USB tuner? I did a little searching, but don’t really get the difference between a PVR/DVR/etc.

I see a lot of support issues with PVR apps on this forum (TVHeadend, etc) are those strictly for playing, or also recording on the RPI?

Can I record broadcast TV at a decent quality with a RPI2 or 3 and a USB TV tuner, or do I need to use a more powerful system, and if the RPI can do it, what USB Tuner is recommended for compatibility and performance? Does the Pi or the TV Tuner do the actual encoding?