Is there any relation to the two plots?

Today we met the second group of awkwardly simple characters. Cop 633 (Tony Leung Chiu Wai) and Faye (Faye Wong) act out a pitiful yet romantic ballet of depression, awkward moments, and series of silences all with the background of the Mama’s and the Papa’s song “California Dreamin’.” This second plot is not nearly as dark and ominous as the one that precedes it. Wong Kar-Wai, the film’s director, clearly shows this distinction through the change in the music as well as the change in the cinematographic techniques. In the first story there are many subtexts to the main plot that dive deep into the lives of the characters. For example, the woman with the blonde wig is a big time drug trafficker who has women dressing like her and cop 223 actually does cop work, arresting people. If you notice in the second story, cop 633 does nothing but dawn an officer’s uniform to signify his role as a man of law. I just thought that was an interesting parallel between the two plots. Also in the first story there are so many undeveloped parts. We never see cop 223’s May, we only hear about her and we never find out what happens at the bar between the woman in the wig and cop 223. However, in the second story things are much simpler. We see everything that goes on, to an extent. And although we are not certain if cop 633 and Faye get together, we can assume by their dialogue and their actions that there is some progression in their relationship.