Both the Serverless and Microservices reduce the time to market. Microservices is a technical term where as serverless has more a marketing term like the Cloud has when compared to virtualiation. Essentially, both Serverless and Microservices allow handling changing requirements with lesser effort which results lowering of the operation costs in the environments with larger load. Microservices are a specific way to build service oriented architectures. The services tend to be smaller and the protocols are lightweight. REST with JSON for example are very common protocols in a microservice architecture, so as AMQP. Serverless architectures consist of different concepts such as Function as a Service (FaaS).
In a microservice architecture, the solutions are provided by a system are divided into tiny-sized service applications instead of monolithic, larger services with complex APIs. If we are building an e-commerce back-end then we can build a service that will have an API with all the necessary functionality from payment processing to shipment tracking. We can also approach to solve the same problem by designing several micro-sized services, such as an authentication/authorization service, a payment service, an inventory service, etc. Division of the larger service into separate smaller services having a system architecture with independently-scalable components which are running as separate services.
Serverless refers to a system where deployment of a software service is done on a cloud based platform. Serverless architectures are more efficient in sharing resources. Who develop and deploy a service are not interested in the underlying infrastructure. FaaS customers pay for the execution count of a function in contrast to microservices, where they pay for running processes regardless whether there is some load or not. Serverless Computing is the process of utilizing 3rd party cloud services like IBM OpenWhisk, AWS Lambda, DynamoDB and API Gateway in order to not maintain our own servers.
So, we have understood that while Serverless and Microservices are not related with each other. Microservices can be used to build a Serverless architecture and Serverless architecture can be used in Microservices.