Yes, you need both — they serve completely different purposes. Your visa (like the Visa on Arrival or C1) is your legal permission to enter and stay in Indonesia.
The All Indonesia Arrival Card is a separate, digital form covering customs and health declarations that every traveler must complete, regardless of visa type, within 72 hours before arrival. Having a valid visa doesn't exempt you from the Arrival Card, and filling out the Arrival Card doesn't replace the need for a visa.