Both documents matter for a rental, and new tenants and first-time landlords sometimes assume one can substitute for the other. They can't — each answers a completely different question.
A lease agreement is the rulebook
It sets out the terms both sides agreed to at the start: rent amount, duration, deposit, responsibilities, rules around subletting or pets, and what happens at the end of the tenancy. It's signed once (or renewed periodically) and governs the relationship as a whole.
A rent receipt is proof of a single transaction
Each receipt confirms one specific payment happened — this amount, on this date, for this month. It doesn't establish the terms of the tenancy; it just documents that one obligation under the lease was fulfilled.
Why you need both, not either
A lease without receipts leaves no record of whether the agreed terms were actually followed month to month. Receipts without a lease leave no record of what was actually agreed to in the first place — like proof of payment for terms nobody wrote down.
When each one actually gets used
A dispute about whether rent has increased without agreement, or what's included in the rent, points back to the lease. A dispute about whether a specific month was paid points to the receipts. Different documents, different questions.