A useful way in understanding differences is in how they technically connect private resources to public services.
Gateway Endpoints route traffic by adding prefix lists within a VPC route table which targets the Gateway endpoint. It is a logical gateway object similar to a Internet Gateway.
In contrast, an Interface Endpoint uses Privatelink to inject into a VPC at the subnet level, via an Elastic Network Interface (ENI), giving network interface functionality, and therefore, DNS and private IP addressing as a means to connect to AWS public services, rather than simply being routed to it.
The differences in connections offer differing advantages and disadvantages (availability, resiliency, access, scalability, and etc), which then dictates how best to connect private resources to public services.
Privatelink is simply a very much abstracted technology to allow a more simplified connection by using DNS. The following AWS re:Invent offers a great overview of Privatelink: https://www.youtube.com/watch?v=abOFqytVqBU