iPhone workout app not showing max heart rate correctly from Apple watch

I have an iPhone 15 pro and an Apple Watch Series 9. All updates are current. My workout app on the iPhone reports a lower max heart rate than the Apple Watch displayed during the workout. For example, during my recent workout my Apple Watch showed my max heart rate was 151 while I was working out on the stair climber. After the workout, I checked the workout app on my iPhone, and it showed my max heart rate during the stair climber workout as 138.

Why the difference?