The decision to (a) create separate indices on a single application or (b) create separate applications depends primarily on the level of isolation needed between your different websites.
For current plans, there are no restrictions in Algolia to prevent you from using one application across multiple domains. The choice is entirely up to you. *
The documentation below (which refers to multiple "environments" but equally applies to multiple websites/domains) provides additional details for each solution that may help you to determine the best approach for your websites:
* Some legacy plans (before July 1, 2020) require a separate license or plan for each domain and legal entity. Please refer to your service order or contact us at our help centre if you are unsure of your plan’s requirements.