How should the wāw be contrasted in “Zayd entered and the lesson began” versus “Zayd entered while his face smiled”?

Supplementary Practice 7: Editing Expressions, Weighing Context and Rhetorical Critique

• Both are invariably oath particles
• The first coordinates independent events; the second links a circumstance
• Both merely repeat an assertion
• The first must be circumstantial and the second unrelated