A product can share its purpose across platforms without sharing every interaction. A thumb on a small screen and a cursor on a large display come with different expectations.
Begin with the task, then decide how each device can support it. Navigation, touch targets, text density and feedback all deserve attention at the platform level.
Shared components are useful where the behavior is truly shared. Where it differs, a deliberate platform-specific choice can keep the experience familiar.
The goal is continuity: people should recognize the product and understand what to do next, even when the controls change.