If you're building against Dynamics 365 Sales, Customer Service, or another Dataverse-based app, you're working with the Dataverse Web API: OData v4, authenticated through Azure Active Directory, able to read or write almost any entity in the system, including custom ones. Business Central runs on different underlying technology and ships its own REST API with its own API pages and authentication setup, built separately from Dataverse's.
Older, on-premises versions of Dynamics CRM (2011 through roughly 2015) used a different setup entirely, mostly SOAP-based calls to the Organization Service, before Microsoft introduced the modern Web API. Microsoft has been retiring that legacy endpoint over time, so an integration built years ago against old Dynamics CRM web services usually needs rebuilding against the current Dataverse Web API, not just a connection-string update.