In a distributed architecture, an API gateway and a service mesh serve distinct but complementary roles. The API gateway manages "north-south" traffic, which is the communication between external clients and the application's edge. In contrast, a service mesh is specifically designed to manage "east-west" traffic, which is the internal, service-to-service communication within the distributed application. It provides a dedicated infrastructure layer for features like service discovery, load balancing, encryption, and observability for these internal interactions, decoupling these concerns from the application logic itself.

B. Between the application and external API implementations: This describes egress traffic control, which is a secondary function and not the primary purpose of a service mesh, which focuses on internal communication.

C. Between the application and external API clients: This is the primary role of an API gateway (managing "north-south" traffic), not a service mesh.

D. Between application services and the firewall: A service mesh operates at the application layer to manage service interactions, not as a direct intermediary to a network firewall.

1. MuleSoft Official Blog, "API gateway vs. service mesh: What's the difference?": This document explicitly distinguishes the roles. It states, "A service mesh is a dedicated infrastructure layer for facilitating service-to-service communications between microservices... A service mesh manages east-west traffic... An API gateway is a tool for managing north-south traffic, which is traffic that goes in and out of the cluster." (MuleSoft, a Salesforce Company. Published May 20, 2022).

2. MuleSoft Documentation, "Anypoint Service Mesh Overview": The documentation describes Anypoint Service Mesh as a tool to "manage and secure your microservices from a single pane of glass," emphasizing its role in governing the interactions between microservices, which constitutes the internal communication fabric of the application. (MuleSoft Documentation, Anypoint Platform, Service Mesh 1.3).

3. MuleSoft Documentation, "API Gateway": The official documentation defines the API Gateway's role as the component that "sits in front of your APIs and enforces your policies," confirming its position at the edge of the application to handle incoming client requests. (MuleSoft Documentation, Anypoint Platform, API Gateway).