The main challenge for audio streaming is to have the data sent without any interruption. Having a song buffer half way playing would be bad for business. To do this, you have to make sure that the transfer of data is as small as possible, taking into account that internet transfer speed isn’t consistent in most places in the world.
To make things simple, the smaller the size, the bigger the compromise on the quality.
There are many measurements in digital audio format. What you mentioned is Hz is the measurement for the sampling rate (example like meter is for distance), which is one of the many measurements. For this discussion in relation to Spotify, we will look at the measurement in bit-rates (google if you want to find out more about digital audio and its measurements)

Here’s what Spotify uses:

Do note the higher quality you choose, it’s recommended to have a higher internet speed (or please select the available offline mode to download it first so it doesn’t stream).

Can you hear the difference? To me, yes, very much. But it differs from people I guess. An example is some people do watch movies in DVD and they’re happy but there’s BlueRay, then there’s 4k format that’s even higher.
You do need some nice headphones or speakers to hear the difference. For me I was disappointed with the so called Premium Spotify quality, but then again I understand as their main subsribers are just average consumers with average headphones who care more about the huge variety of choice rather than sound quality. Well, for the insanely dirt cheap price for a whole collection of songs and albums at 320kpbs I think its alright.
I subscribe to Spotify for on the go listening but if I like an album I’ll purchase it separately. If you are serious on audio quality do check out hdtracks.com. Bandcamp does offer high quality stuff too with extra freebies and I always donate extra directly to the artists.