All of these channels are compressed. That's what H.264 and H.265 are: compression systems, or "codecs" (coder, decoder).
What you're seeing on NBC and PBS is less compression. An uncompressed HD signal inside NBC is probably in the hundreds of megabits per second, if not 1Gbps. But that's unwieldy for broadcast.
As the feeds are destined for TV stations and over-the-air broadcast, less compression is used to keep the signal quality as high as possible.
Velocity is probably fed to Dish Network at a higher bit rate and Dish compresses it down to 3Mbps so it takes up less space and they can fit more channels in.
This is also why an over the air signal from your antenna will usually be superior to the same signal via cable, Dish or DirecTV. Pay TV service providers compress signals more aggressively to get more channels in.
H.264 has been around for a few years and is widely used but not as efficient as the newer H.265, but many set top boxes and TVs don't have the H.265 codec inside so they cannot decode it.
That's why your STB interpreted the HEVC channel as radio - because it has the audio codec but not the H.265 video codec.
Picture quality is determined by how aggressively compression is applied. To complicate matters, many providers use variable bit rate coding if they have a set of channels being broadcast together. So if channel 1 is broadcasting, say, the news where there are many seconds of images of a news reader that don't change much and channel 2 is broadcasting an NFL game where the picture is always changing, the encoder can give a bit less bandwidth to channel 1 and a bit more to channel 2. It's dynamic and changes all the time but more efficient.
With the advent of 4K broadcasting, the streams require more bandwidth and H.265 does a better job of compressing this down so is being introduced with the new format.
That's why some STBs erroneously assume all H.265 is 4K. You sometimes see the same with STBs that assume all 16:9 or H.264 content is high-definition, as noted above, when sometimes it's not. That's just sloppy programming.