A message broker is a software or tool that guides communication across services or parts of an architecture.
A queue is a sequential data store that keeps track of the order of insertion of its items.
Message brokers are products that we use in data engineering or backend development.
While queues are an abstraction of how data or items can be arranged.

A message broker coordinates the flow of data (or messages). It is an essential component of every data-rich system. It is asynchronous.
It can hold messages even if those messages’ intended recipients are unavailable.
It can use a publisher/subscriber pattern or a producer/consumer pattern. Examples of message brokers include Kafka, RabbitMQ, Memphis.dev, etc.

A queue is a data structure with openings at its two ends. In a queue, data or items only enter through its tail (or end) and leave through its head (or beginning).
That is, as a sequential data structure, the first item to enter a queue is the first item to leave.
A real-life example of a queue is the line of people trying to board a plane.
As people are in the line, those who had first lined up (or queued up) enter the plane before those queuing up later.