Assuming the Apple Fitness+ subscription is available to both: —
When used at different times, the person can connect their own Apple Watch to start the workout.
When used at the same time, one can connect, and the other can tag along (without on-screen metrics), and track their own activity on their own Apple Watch.
If one of you subscribes, then the other can also access Fitness+ through Family Sharing (=grouping Apple IDs to share certain services). If you haven’t configured that yet, then read on:
About Family Sharing - Apple
Learn more about what you can do with Family Sharing - Apple Support
Set up Family Sharing - Apple Support
Add a family member to your shared subscriptions - Apple Support
What types of content can I share with my family? - Apple Support