The short answer is no. Customer engagement may lead to retention, but they are not the same thing.
Customer engagement is what you are doing to involve your customers in your business. However, the objective of engagement is not just to retain the customer, it is much broader. Engagement can be used to improve products and services, increase brand awareness, grow the business through creating customers who are brand ambassadors or even accelerate the sales cycle, whereas retention focuses on keeping customers loyal in their use of your products and services.
It is an important distinction to make when developing strategies around customer stratification and engagement. Consider the desired outcome of the strategy before developing it. Are you looking to grow your business with one particular customer or in the overall marketplace?