The New Music Mix only releases one playlist a week. I believe Discover Weekly releases five playlists a week, each with their own moods. I much prefer Spotify's approach.
However I do find that both services largely recommend the same music to me. They just have different mechanisms of surfacing it.
Discover Weekly is once a week: on Mondays.
You're thinking of Daily Mixes, of which there are 6 that update throughout the week, one playlist per day.
To go along with Discover Weekly there's also a Release Radar playlist that updates every Friday with that week's new releases from your artists.
Spotify is so deeply engrained into my weekly schedule that I really look forward to the Discover Weekly and Release Radar playlists bookending my work weeks.
However I do find that both services largely recommend the same music to me. They just have different mechanisms of surfacing it.