Sinatra vs. Rails API

Sinatra is a DSL for quickly creating web applications in Ruby with minimal effort.

Rails::API is a subset of a normal Rails application, created for applications that don't require all functionality that a complete Rails application provides. It is a bit more lightweight, and consequently a bit faster than a normal Rails application. The main example for its usage is in API applications only, where you usually don't need the entire Rails middleware stack nor template generation.