Wednesday night at Radio City Music Hall, Billie Eilish was cavorting in a universe of her own design. On the screens behind her were crawling insects, a baby doll engulfed in flames, gloomy silhouettes of barren trees . Her hair was dyed a deep black, with tones of green and purple peeking through. For much of the show, the lighting was broodingly dark and pierced by intense strobes, and she commanded the room alone but for two musicians dressed unobtrusively in all white .

The night before at Madison Square Garden, Ariana Grande delivered a fantasia, too. Tautly controlled dance sequences. Small acts of kiss-off theater. With her hair clutched high into her signature ponytail, and wearing shimmering outfits with shoulders that pointed skyward to the cheap seats, she was part 1950s and part 2050s .

From a distance, Grande and Eilish represent two divergent approaches to pop superstardom. Grande is chromed and polished, a laser-precise, big-voiced, old-fashioned maximalist; Eilish is offbeat and earthy, with an almost shrugging approach to fame and a voice that sometimes remains at the level of a conspiratorial whisper.