It is easier to think about them if you realize they aren’t mutually exclusive. Think of an API gateway as a specific type reverse proxy implementation.
In regards to your questions, it is not uncommon to see both used in conjunction where the API gateway is treated as an application tier that sits behind a reverse proxy for load balancing and health checking. An example would be something like a WAF sandwich architecture in that your Web Application Firewall/API Gateway is sandwiched by reverse proxy tiers, one for the WAF itself and the other for the individual microservices it talks to.
Regarding the differences, they are very similar. It’s just nomenclature. As you take a basic reverse proxy setup and start bolting on more pieces like authentication, rate limiting, dynamic config updates, and service discovery, people are more likely to call that an API gateway.