The scene is Capernaum, the synagogue at Capernaum, that town of about 2000 people on the northern shore of the Lake of Tiberius. This incident shows the total necessity of faith.
Does Luke force us to see this as a different day, when Matthew 12:9a implies it was the same day? Yes. Although Matthew 12:9 must follow on from Matthew 12:8, Luke makes clear this is not the same day but another Sabbath day.