Definitions
A casino API is any programmatic interface that lets a platform list, launch and settle casino games. A game aggregator is a business and architecture that connects many game providers and re-exposes their content through one API.
How they relate
An aggregator is one way to deliver a casino API. A casino API can also be a single provider's own interface. When people say 'casino API' they usually mean the integration surface; when they say 'aggregator' they usually mean the multi-provider sourcing model behind it.
What to evaluate
Judge the API on integration quality — wallet semantics, documentation, error handling. Judge the aggregator on sourcing — certified coverage in your markets, commercial terms and content operations.