To remain in a particular place or state.

रहना

English Usage: Please stay here until I return.

Hindi Usage: कृपया यहाँ रहना जब तक मैं लौटूँ।

A state of remaining in a specified position or condition.

ठहरना

English Usage: His stay at the hotel was very pleasant.

Hindi Usage: होटल में उसका ठहरना बहुत सुखद था।